{"title":"Fujita-Type Blow-Up for Discrete Reaction–Diffusion Equations on Networks","authors":"Soon‐Yeong Chung, Min-Jun Choi, Jea-Hyun Park","doi":"10.4171/PRIMS/55-2-1","DOIUrl":"https://doi.org/10.4171/PRIMS/55-2-1","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-2-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46970391","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}
{"title":"Weak Triebel–Lizorkin Spaces with Variable Integrability, Summability and Smoothness","authors":"Wenchang Li, Jingshi Xu","doi":"10.4171/PRIMS/55-2-2","DOIUrl":"https://doi.org/10.4171/PRIMS/55-2-2","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-2-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49046877","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}
{"title":"Quotient Families of Elliptic Curves Associated with Representations of Dihedral Groups","authors":"Ryota Hirakawa, Shigeru Takamura","doi":"10.4171/PRIMS/55-2-4","DOIUrl":"https://doi.org/10.4171/PRIMS/55-2-4","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-2-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43608932","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}
We show that the Kirillov--Reshetikhin crystal $B^{r,s}$ exists when $r$ is a node such that the Kirillov--Reshetikhin module $W^{r,s}$ has a multiplicity free classical decomposition.
{"title":"Existence of Kirillov–Reshetikhin Crystals for Multiplicity-Free Nodes","authors":"Rekha Biswal, Travis Scrimshaw","doi":"10.4171/PRIMS/56-4-4","DOIUrl":"https://doi.org/10.4171/PRIMS/56-4-4","url":null,"abstract":"We show that the Kirillov--Reshetikhin crystal $B^{r,s}$ exists when $r$ is a node such that the Kirillov--Reshetikhin module $W^{r,s}$ has a multiplicity free classical decomposition.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45908847","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}
In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s_lambda(t)$ by certain shifts of arguments. In the present paper we give a simpler proof of this result, using the (1-component) boson-fermion correspondence. Moreover, we show that this approach can be applied to the s-component KP hierarchy, using the s-component boson-fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the s-component KP hierarchy, associated to any partition consisting of s positive parts.
{"title":"Polynomial Tau-Functions for the Multicomponent KP Hierarchy","authors":"V. Kac, J. Leur","doi":"10.4171/prims/58-1-1","DOIUrl":"https://doi.org/10.4171/prims/58-1-1","url":null,"abstract":"In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s_lambda(t)$ by certain shifts of arguments. In the present paper we give a simpler proof of this result, using the (1-component) boson-fermion correspondence. Moreover, we show that this approach can be applied to the s-component KP hierarchy, using the s-component boson-fermion correspondence, finding thereby all its polynomial tau-functions. We also find all polynomial tau-functions for the reduction of the s-component KP hierarchy, associated to any partition consisting of s positive parts.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41508336","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}
Let $X$, $D$ be a smooth projective surface and a simple normal crossing divisor on $X$, respectively. Suppose $kappa (X, K_X + D)ge 0$, let $C$ be an irreducible curve on $X$ whose support is not contained in $D$ and $alpha$ a rational number in $ [ 0, 1 ]$. Following Miyaoka, we define an orbibundle $mathcal{E}_alpha$ as a suitable free subsheaf of log differentials on a Galois cover of $X$. Making use of $mathcal{E}_alpha$ we prove a Bogomolov-Miyaoka-Yau inequality for the couple $(X, D+alpha C)$. Suppose moreover that $K_X+D$ is big and nef and $(K_X+D)^2 $ is greater than $e_{Xsetminus D}$, namely the topological Euler number of the open surface $Xsetminus D$. As a consequence of the inequality, by varying $alpha$, we deduce a bound for $(K_X+D)cdot C)$ by an explicit function of the invariants: $(K_X+D)^2$, $e_{Xsetminus D}$ and $e_{C setminus D} $, namely the topological Euler number of the normalization of $C$ minus the points in the set theoretic counterimage of $D$. We finally deduce that on such surfaces curves with $- e_{Csetminus D}$ bounded form a bounded family, in particular there are only a finite number of curves $C$ on $X$ such that $- e_{Csetminus D}le 0$.
{"title":"An Explicit Bound for the Log-Canonical Degree of Curves on Open Surfaces","authors":"Pietro Sabatino","doi":"10.4171/prims/58-4-6","DOIUrl":"https://doi.org/10.4171/prims/58-4-6","url":null,"abstract":"Let $X$, $D$ be a smooth projective surface and a simple normal crossing divisor on $X$, respectively. Suppose $kappa (X, K_X + D)ge 0$, let $C$ be an irreducible curve on $X$ whose support is not contained in $D$ and $alpha$ a rational number in $ [ 0, 1 ]$. Following Miyaoka, we define an orbibundle $mathcal{E}_alpha$ as a suitable free subsheaf of log differentials on a Galois cover of $X$. Making use of $mathcal{E}_alpha$ we prove a Bogomolov-Miyaoka-Yau inequality for the couple $(X, D+alpha C)$. Suppose moreover that $K_X+D$ is big and nef and $(K_X+D)^2 $ is greater than $e_{Xsetminus D}$, namely the topological Euler number of the open surface $Xsetminus D$. As a consequence of the inequality, by varying $alpha$, we deduce a bound for $(K_X+D)cdot C)$ by an explicit function of the invariants: $(K_X+D)^2$, $e_{Xsetminus D}$ and $e_{C setminus D} $, namely the topological Euler number of the normalization of $C$ minus the points in the set theoretic counterimage of $D$. We finally deduce that on such surfaces curves with $- e_{Csetminus D}$ bounded form a bounded family, in particular there are only a finite number of curves $C$ on $X$ such that $- e_{Csetminus D}le 0$.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46732011","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}
{"title":"On the Stokes Geometry of a Unified Family of $P_mathrm J$-Hierarchies (J=I, II, IV, 34)","authors":"Yoko Umeta","doi":"10.4171/PRIMS/55-1-3","DOIUrl":"https://doi.org/10.4171/PRIMS/55-1-3","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-1-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48800741","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}
A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra hat{g}_{-kappa} at a negative level -kappa and the category Rep_q(G) of (algebraic) representations of the "big" (a.k.a. Lusztig's) quantum group. In this paper we propose a conjecture that describes the category of Iwahori-integrable Kac-Moody modules. The corresponding object on the quantum group side, denoted Rep^{mxd}_q(G), involves Lusztig's version of the quantum group for the Borel and the De Concini-Kac version for the negative Borel.
{"title":"A Conjectural Extension of the Kazhdan–Lusztig Equivalence","authors":"D. Gaitsgory","doi":"10.4171/prims/57-3-14","DOIUrl":"https://doi.org/10.4171/prims/57-3-14","url":null,"abstract":"A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra hat{g}_{-kappa} at a negative level -kappa and the category Rep_q(G) of (algebraic) representations of the \"big\" (a.k.a. Lusztig's) quantum group. In this paper we propose a conjecture that describes the category of Iwahori-integrable Kac-Moody modules. The corresponding object on the quantum group side, denoted Rep^{mxd}_q(G), involves Lusztig's version of the quantum group for the Borel and the De Concini-Kac version for the negative Borel.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41770265","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}
{"title":"Pro-$p$ Grothendieck Conjecture for Hyperbolic Polycurves","authors":"K. Sawada","doi":"10.4171/PRIMS/54-4-3","DOIUrl":"https://doi.org/10.4171/PRIMS/54-4-3","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/54-4-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42970272","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}
We prove exactness of parabolic restriction and induction functors for conjugation equivariant sheaves on a reductive group generalizing a well known result of Lusztig who established this property for character sheaves. We propose a conjectural (but known for character sheaves) t-exactness property of the Harish-Chandra transform and provide an evidence for that conjecture. We also present two applications generalizing some results of Gabber and Loeser on perverse sheaves on an algebraic torus to an arbitrary reductive group.
{"title":"On Parabolic Restriction of Perverse Sheaves","authors":"R. Bezrukavnikov, Alexander Yom Din","doi":"10.4171/prims/57-3-12","DOIUrl":"https://doi.org/10.4171/prims/57-3-12","url":null,"abstract":"We prove exactness of parabolic restriction and induction functors for conjugation equivariant sheaves on a reductive group generalizing a well known result of Lusztig who established this property for character sheaves. We propose a conjectural (but known for character sheaves) t-exactness property of the Harish-Chandra transform and provide an evidence for that conjecture. We also present two applications generalizing some results of Gabber and Loeser on perverse sheaves on an algebraic torus to an arbitrary reductive group.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44906550","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}
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