Pub Date : 2024-07-03DOI: 10.1017/s1474748024000173
Paweł Nurowski
In Cartan’s PhD thesis, there is a formula defining a certain rank 8 vector distribution in dimension 15, whose algebra of authomorphism is the split real form of the simple exceptional complex Lie algebra $mathfrak {f}_4$ . Cartan’s formula is written in the standard Cartesian coordinates in $mathbb {R}^{15}$ . In the present paper, we explain how to find analogous formulae for the flat models of any bracket generating distribution $mathcal D$ whose symbol algebra $mathfrak {n}({mathcal D})$ is constant and 2-step graded, $mathfrak {n}({mathcal D})=mathfrak {n}_{-2}oplus mathfrak {n}_{-1}$ . The formula is given in terms of a solution to a certain system of linear algebraic equations determined by two representations $(rho ,mathfrak {n}_{-1})$ and $(tau ,mathfrak {n}_{-2})$ of a Lie algebra $mathfrak {n}_{00}$ contained in the
{"title":"EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS","authors":"Paweł Nurowski","doi":"10.1017/s1474748024000173","DOIUrl":"https://doi.org/10.1017/s1474748024000173","url":null,"abstract":"In Cartan’s PhD thesis, there is a formula defining a certain rank 8 vector distribution in dimension 15, whose algebra of authomorphism is the split real form of the simple exceptional complex Lie algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline3.png\"/> <jats:tex-math> $mathfrak {f}_4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Cartan’s formula is written in the standard Cartesian coordinates in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline4.png\"/> <jats:tex-math> $mathbb {R}^{15}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In the present paper, we explain how to find analogous formulae for the flat models of any bracket generating distribution <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline5.png\"/> <jats:tex-math> $mathcal D$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose symbol algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline6.png\"/> <jats:tex-math> $mathfrak {n}({mathcal D})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is constant and 2-step graded, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline7.png\"/> <jats:tex-math> $mathfrak {n}({mathcal D})=mathfrak {n}_{-2}oplus mathfrak {n}_{-1}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. The formula is given in terms of a solution to a certain system of linear algebraic equations determined by two representations <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline8.png\"/> <jats:tex-math> $(rho ,mathfrak {n}_{-1})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline9.png\"/> <jats:tex-math> $(tau ,mathfrak {n}_{-2})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of a Lie algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline10.png\"/> <jats:tex-math> $mathfrak {n}_{00}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> contained in the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline11.png\"/> <jats:tex-math>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-28DOI: 10.1017/s1474748024000082
Damien Junger
Résumé Dans cet article, nous étudions la cohomologie de de Rham du premier revêtement de la tour de Drinfel’d. En particulier, nous obtenons une preuve purement locale du fait que la partie supercuspidale réalise la correspondance de Jacquet-Langlands locale pour $mathrm {GL}_n$ en la comparant à la cohomologie rigide de certaines variétés de Deligne-Lusztig. Les représentations obtenues sont analogues à celles qui apparaissent dans la cohomologie $ell $ -adique lorsqu’on oublie l’action du groupe de Weil. La preuve repose sur une généralisation d’un résultat d’excision de Grosse-Klönne et de la description explicite du premier revêtement en tant que revêtement cyclique obtenu par l’auteur dans un travail précédent.
{"title":"COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD","authors":"Damien Junger","doi":"10.1017/s1474748024000082","DOIUrl":"https://doi.org/10.1017/s1474748024000082","url":null,"abstract":"Résumé Dans cet article, nous étudions la cohomologie de de Rham du premier revêtement de la tour de Drinfel’d. En particulier, nous obtenons une preuve purement locale du fait que la partie supercuspidale réalise la correspondance de Jacquet-Langlands locale pour <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000082_inline3.png\"/> <jats:tex-math> $mathrm {GL}_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> en la comparant à la cohomologie rigide de certaines variétés de Deligne-Lusztig. Les représentations obtenues sont analogues à celles qui apparaissent dans la cohomologie <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000082_inline4.png\"/> <jats:tex-math> $ell $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-adique lorsqu’on oublie l’action du groupe de Weil. La preuve repose sur une généralisation d’un résultat d’excision de Grosse-Klönne et de la description explicite du premier revêtement en tant que revêtement cyclique obtenu par l’auteur dans un travail précédent.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-24DOI: 10.1017/s1474748024000197
Rui Chen, Wee Teck Gan
In this paper, we investigate the twisted GGP conjecture for certain tempered representations using the theta correspondence and establish some special cases, namely when the L-parameter of the unitary group is the sum of conjugate-dual characters of the appropriate sign.
在本文中，我们利用 Theta 对应关系研究了某些调和表示的扭曲 GGP 猜想，并建立了一些特例，即当单元群的 L 参数是适当符号的共轭双字符之和时的特例。
{"title":"TWISTED GAN–GROSS–PRASAD CONJECTURE FOR CERTAIN TEMPERED L-PACKETS","authors":"Rui Chen, Wee Teck Gan","doi":"10.1017/s1474748024000197","DOIUrl":"https://doi.org/10.1017/s1474748024000197","url":null,"abstract":"In this paper, we investigate the twisted GGP conjecture for certain tempered representations using the theta correspondence and establish some special cases, namely when the L-parameter of the unitary group is the sum of conjugate-dual characters of the appropriate sign.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-17DOI: 10.1017/s1474748024000227
Peter Humphries
We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman–Wallach representation of $operatorname {mathrm {GL}}_n(F)$ , where F is an archimedean local field, that quantifies the extent to which this representation may be ramified. We also determine a distinguished vector, the newform, occurring with multiplicity one in this representation, with the complexity of this vector measured in a natural way by the conductor exponent. Finally, we show that the newform is a test vector for $operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_n$ and $operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_{n - 1}$ Rankin–Selberg integrals when the second representation is unramified. This theory parallels an analogous nonarchimedean theory due to Jacquet, Piatetski-Shapiro, and Shalika; combined, this completes a global theory of newforms for automorphic representations of $operatorname {mathrm {GL}}_n$ over number fields. By-products of the proofs include new proofs of Stade’s formulæ and a new resolution of the test vector problem for archimedean Godement–Jacquet zeta integrals.
我们为 $operatorname {mathrm {GL}}_n(F)$ （其中 F 是一个阿基米德局部场）的一般不可还原卡塞尔曼-瓦拉几表示引入了一个新的不变量--导体指数，它量化了这个表示可能被夯实的程度。我们还确定了一个杰出的向量--新形式，它在这个表示中出现的倍率为 1，这个向量的复杂性可以用导体指数来自然地衡量。最后，我们证明了当第二个表示没有ramified时，新形式是 $operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_n$ 和 $operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_{n - 1}$ 兰金-塞尔伯格积分的检验向量。这一理论与雅克特（Jacquet）、皮亚特斯基-沙皮罗（Piatetski-Shapiro）和沙利卡（Shalika）提出的类似的非archimedean理论相似；结合起来，就完成了数域上$operatorname {mathrm {GL}}_n$ 的自变态表示的新形态全局理论。这些证明的副产品包括对斯塔德公式的新证明，以及对拱顶戈德门-雅克特zeta积分的检验向量问题的新解决。
{"title":"ARCHIMEDEAN NEWFORM THEORY FOR","authors":"Peter Humphries","doi":"10.1017/s1474748024000227","DOIUrl":"https://doi.org/10.1017/s1474748024000227","url":null,"abstract":"\u0000 We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman–Wallach representation of \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n(F)$\u0000\u0000 \u0000 , where F is an archimedean local field, that quantifies the extent to which this representation may be ramified. We also determine a distinguished vector, the newform, occurring with multiplicity one in this representation, with the complexity of this vector measured in a natural way by the conductor exponent. Finally, we show that the newform is a test vector for \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_n$\u0000\u0000 \u0000 and \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n times operatorname {mathrm {GL}}_{n - 1}$\u0000\u0000 \u0000 Rankin–Selberg integrals when the second representation is unramified. This theory parallels an analogous nonarchimedean theory due to Jacquet, Piatetski-Shapiro, and Shalika; combined, this completes a global theory of newforms for automorphic representations of \u0000 \u0000 \u0000 \u0000$operatorname {mathrm {GL}}_n$\u0000\u0000 \u0000 over number fields. By-products of the proofs include new proofs of Stade’s formulæ and a new resolution of the test vector problem for archimedean Godement–Jacquet zeta integrals.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140962654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.1017/s1474748024000203
{"title":"JMJ volume 23 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1474748024000203","DOIUrl":"https://doi.org/10.1017/s1474748024000203","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141046831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.1017/s1474748024000215
{"title":"JMJ volume 23 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1474748024000215","DOIUrl":"https://doi.org/10.1017/s1474748024000215","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141042266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.1017/s1474748024000069
J. Hornbostel, Doosung Park
{"title":"ADDENDUM: REAL TOPOLOGICAL HOCHSCHILD HOMOLOGY OF SCHEMES","authors":"J. Hornbostel, Doosung Park","doi":"10.1017/s1474748024000069","DOIUrl":"https://doi.org/10.1017/s1474748024000069","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141054940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-25DOI: 10.1017/s1474748024000021
Gebhard Böckle, Chandrashekhar B. Khare, Jeffrey Manning
In his work on modularity of elliptic curves and Fermat’s last theorem, A. Wiles introduced two measures of congruences between Galois representations and between modular forms. One measure is related to the order of a Selmer group associated to a newform $f in S_2(Gamma _0(N))$ (and closely linked to deformations of the Galois representation $rho _f$ associated to f), whilst the other measure is related to the congruence module associated to f (and is closely linked to Hecke rings and congruences between f and other newforms in $S_2(Gamma _0(N))$ ). The equality of these two measures led to isomorphisms $R={mathbf T}$ between deformation rings and Hecke rings (via a numerical criterion for isomorphisms that Wiles proved) and showed these rings to be complete intersections. We continue our study begun in [BKM21] of the Wiles defect of deformation rings and Hecke rings (at a newform f) acting on the cohomology of Shimura curves over ${mathbf Q}$ : It is defined to be the difference between these two measures of congruences. The Wiles defect thus arises from the failure of the Wiles numerical criterion at an augmentation $lambda _f:{mathbf T} to {mathcal O}$ . In situations we study here, the Taylor–Wiles–Kisin patching method gives an isomorphism
{"title":"WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS","authors":"Gebhard Böckle, Chandrashekhar B. Khare, Jeffrey Manning","doi":"10.1017/s1474748024000021","DOIUrl":"https://doi.org/10.1017/s1474748024000021","url":null,"abstract":"In his work on modularity of elliptic curves and Fermat’s last theorem, A. Wiles introduced two measures of congruences between Galois representations and between modular forms. One measure is related to the order of a Selmer group associated to a newform <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline1.png\"/> <jats:tex-math> $f in S_2(Gamma _0(N))$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> (and closely linked to deformations of the Galois representation <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline2.png\"/> <jats:tex-math> $rho _f$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> associated to <jats:italic>f</jats:italic>), whilst the other measure is related to the congruence module associated to <jats:italic>f</jats:italic> (and is closely linked to Hecke rings and congruences between <jats:italic>f</jats:italic> and other newforms in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline3.png\"/> <jats:tex-math> $S_2(Gamma _0(N))$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>). The equality of these two measures led to isomorphisms <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline4.png\"/> <jats:tex-math> $R={mathbf T}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> between deformation rings and Hecke rings (via a numerical criterion for isomorphisms that Wiles proved) and showed these rings to be complete intersections. We continue our study begun in [BKM21] of the <jats:italic>Wiles defect</jats:italic> of deformation rings and Hecke rings (at a newform <jats:italic>f</jats:italic>) acting on the cohomology of Shimura curves over <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline5.png\"/> <jats:tex-math> ${mathbf Q}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>: It is defined to be the difference between these two measures of congruences. The Wiles defect thus arises from the failure of the Wiles numerical criterion at an augmentation <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline6.png\"/> <jats:tex-math> $lambda _f:{mathbf T} to {mathcal O}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In situations we study here, the Taylor–Wiles–Kisin patching method gives an isomorphism <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-17DOI: 10.1017/s1474748024000094
Finn Bartsch, Ariyan Javanpeykar
Kobayashi–Ochiai proved that the set of dominant maps from a fixed variety to a fixed variety of general type is finite. We prove the natural extension of their finiteness theorem to Campana’s orbifold pairs.
{"title":"KOBAYASHI-OCHIAI’S FINITENESS THEOREM FOR ORBIFOLD PAIRS OF GENERAL TYPE","authors":"Finn Bartsch, Ariyan Javanpeykar","doi":"10.1017/s1474748024000094","DOIUrl":"https://doi.org/10.1017/s1474748024000094","url":null,"abstract":"Kobayashi–Ochiai proved that the set of dominant maps from a fixed variety to a fixed variety of general type is finite. We prove the natural extension of their finiteness theorem to Campana’s orbifold pairs.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-17DOI: 10.1017/s1474748024000185
Paul Broussous
Let $E/F$ be a quadratic unramified extension of non-archimedean local fields and $mathbb H$ a simply connected semisimple algebraic group defined and split over F. We establish general results (multiplicities, test vectors) on ${mathbb H} (F)$ -distinguished Iwahori-spherical representations of ${mathbb H} (E)$ . For discrete series Iwahori-spherical representations of ${mathbb H} (E)$ , we prove a numerical criterion of ${mathbb H} (F)$ -distinction. As an application, we classify the ${mathbb H} (F)$ -distinguished discrete series representations of ${mathbb H} (E)$ corresponding to degree $1$ characters of the Iwahori-Hecke algebra.
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