{"title":"On the groups $[X, Sp(n)]$ with $dim X le 4n+2$","authors":"Tomoaki Nagao","doi":"10.1215/KJM/1250280979","DOIUrl":"https://doi.org/10.1215/KJM/1250280979","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Characteristic cycles of standard modules for the rational Cherednik algebra of type $mathbb{Z}/lmathbb{Z}$","authors":"T. Kuwabara","doi":"10.1215/KJM/1250280980","DOIUrl":"https://doi.org/10.1215/KJM/1250280980","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250280980","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Smith equivalence of real representations of a finite group has been studied by many mathematicians, e.g. J. Milnor, T. Petrie, S. Cappell-J. Shaneson, K. Pawa(cid:1)lowski-R. Solomon. For a given finite group, let the primary Smith set of the group be the subset of real representation ring consisting of all differences of pairs of prime matched, Smith equivalent representations. The primary Smith set was rarely determined for a nonperfect group G besides the case where the primary Smith set is trivial. In this paper we determine the primary Smith set of an arbitrary Oliver group such that a Sylow 2-subgroup is normal and the nilquotient is isomorphic to the direct product of a finite number of cyclic groups of order 2 or 3. In particular, we answer to a problem posed by T. Sumi. recent Smith our present research. The authors are grateful to him for his informing results. They also thank the referee for his pointing out typographical errors. The second author was partially supported by KAKENHI 18540086.
有限群实表示的Smith等价已被许多数学家研究，如J. Milnor, T. Petrie, S. Cappell-J。李建军，李建军，李建军，等。所罗门。对于给定的有限群，设群的初等Smith集合是由素匹配的Smith等价表示对的所有差组成的实表示环的子集。对于非完美群G，除了主Smith集是平凡的情况外，主Smith集很少被确定。本文确定了任意Oliver群的初等Smith集，使得一个Sylow 2-子群是正规的，且nil商同构于有限个2阶或3阶循环群的直积。特别是，我们回答了T. Sumi提出的一个问题。最近史密斯我们目前的研究。作者对他的成果表示感谢。他们还感谢裁判指出了印刷错误。第二作者得到KAKENHI 18540086的部分支持。
{"title":"The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients","authors":"Akihiro Koto, M. Morimoto, Yan Qi","doi":"10.1215/KJM/1250280981","DOIUrl":"https://doi.org/10.1215/KJM/1250280981","url":null,"abstract":"The Smith equivalence of real representations of a finite group has been studied by many mathematicians, e.g. J. Milnor, T. Petrie, S. Cappell-J. Shaneson, K. Pawa(cid:1)lowski-R. Solomon. For a given finite group, let the primary Smith set of the group be the subset of real representation ring consisting of all differences of pairs of prime matched, Smith equivalent representations. The primary Smith set was rarely determined for a nonperfect group G besides the case where the primary Smith set is trivial. In this paper we determine the primary Smith set of an arbitrary Oliver group such that a Sylow 2-subgroup is normal and the nilquotient is isomorphic to the direct product of a finite number of cyclic groups of order 2 or 3. In particular, we answer to a problem posed by T. Sumi. recent Smith our present research. The authors are grateful to him for his informing results. They also thank the referee for his pointing out typographical errors. The second author was partially supported by KAKENHI 18540086.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Malliavin calculus on extensions of abstract Wiener spaces","authors":"Horst Osswald","doi":"10.1215/KJM/1250271411","DOIUrl":"https://doi.org/10.1215/KJM/1250271411","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250271411","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the damped nonlinear Schödinger equation with delta functions as initial data","authors":"K. Doi","doi":"10.1215/KJM/1250271416","DOIUrl":"https://doi.org/10.1215/KJM/1250271416","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mod $p$ decompositions of non-simply connected Lie groups","authors":"D. Kishimoto, A. Kono","doi":"10.1215/KJM/1250280972","DOIUrl":"https://doi.org/10.1215/KJM/1250280972","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250280972","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let g be a complex simple Lie algebra. We have the adjoint representation of the adjoint group G on g . Then G acts on the projective space P g . We consider the closure X of the image of a nilpotent orbit in P g . The i -secant variety Sec ( i ) X of a projective variety X is the closure of the union of projective subspaces of dimension i in the ambient space P spanned by i + 1 points on X . In particular we call the 1-secant variety the secant variety. In this paper we give explicit descriptions of the secant and the higher secant varieties of nilpotent orbits of complex classical simple Lie algebras.
{"title":"The secant varieties of nilpotent orbits","authors":"Yasuhiro Omoda","doi":"10.1215/KJM/1250280975","DOIUrl":"https://doi.org/10.1215/KJM/1250280975","url":null,"abstract":"Let g be a complex simple Lie algebra. We have the adjoint representation of the adjoint group G on g . Then G acts on the projective space P g . We consider the closure X of the image of a nilpotent orbit in P g . The i -secant variety Sec ( i ) X of a projective variety X is the closure of the union of projective subspaces of dimension i in the ambient space P spanned by i + 1 points on X . In particular we call the 1-secant variety the secant variety. In this paper we give explicit descriptions of the secant and the higher secant varieties of nilpotent orbits of complex classical simple Lie algebras.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
If a GriMths domain D is a symmetric Hermitian domain, the toroidal compactification of the quotient space rXD, associated to a projective fan and a discrete subgroup F of Aut(D), was constructed by Mumford et al. Kazuya Kato and Sampei Usui studied extensions of rXD for a GriMths domain D in general, and introduced a notion of "complete fan" as a generalization of a notion of projective fan. The existence of complete fans is expected. In this paper, we give an example of D which has no complete fan.
{"title":"A counterexample to a conjecture of complete fan","authors":"Kenta Watanabe","doi":"10.1215/KJM/1250271324","DOIUrl":"https://doi.org/10.1215/KJM/1250271324","url":null,"abstract":"If a GriMths domain D is a symmetric Hermitian domain, the toroidal compactification of the quotient space rXD, associated to a projective fan and a discrete subgroup F of Aut(D), was constructed by Mumford et al. Kazuya Kato and Sampei Usui studied extensions of rXD for a GriMths domain D in general, and introduced a notion of \"complete fan\" as a generalization of a notion of projective fan. The existence of complete fans is expected. In this paper, we give an example of D which has no complete fan.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Malliavin calculus for functionals of a Poisson random measure has been developed by many authors. Bismut [2] has generalized the Malliavin calculus for Wiener-Poisson functionals by using the Girsanov theorem. As another method, in Bichteler, Gravereaux and Jacod [1], one can find the study of the Malliavin operator on Wiener-Poisson space and application of it to stochastic differential equations. Both in these works, the authors have given differential operators on Wiener-Poisson space and have proved the integration by parts formulas. These formulation suffers some limitation on an intensity measure, that is, the intensity measure must have a smooth density. On the other hand, in the Malliavin calculus for Wiener functionals, Wiener chaos expansion of the space of square integrable Wiener functionals can be considered as a Fock space, and the differential operator is regarded as the annihilation operator on a Fock space. This sort of structure can be also found in the case of the space of square integrable functionals of Wiener-Poisson space, see [6]. Nualart and Vives [10], [11], and Picard [13] have studied the annihilation operator and its dual operator (the creation operator) on the space of square integrable functionals of a Poisson random measure. Picard [12] has also given a smoothness criterion by using the duality formula (see Theorem 2.1) for functionals of a Poisson random measure under the Condition 1 (see Section 2) on the intensity measure, and has studied the solution to some stochastic differential equation. This argument of Picard can be generalized for some Wiener-Poisson functionals, see [5]. The Condition 1 differs from that of [1], and allows us to take a intensity measure with some singularity. One can find some interesting examples satisfying Condition 1, for instance, stable processes and CGMY processes (see [3]). The purpose of this paper is to prove the asymptotic expansion theorem (done in the Wiener space by Watanabe [18]) for functionals of a Poisson random measure. By using the Malliavin operator which we mentioned above, Sakamoto and Yoshida [15] have studied asymptotic expansion formulas of some
{"title":"Asymptotic expansions for functionals of a Poisson random measure","authors":"Masafumi Hayashi","doi":"10.1215/KJM/1250280977","DOIUrl":"https://doi.org/10.1215/KJM/1250280977","url":null,"abstract":"The Malliavin calculus for functionals of a Poisson random measure has been developed by many authors. Bismut [2] has generalized the Malliavin calculus for Wiener-Poisson functionals by using the Girsanov theorem. As another method, in Bichteler, Gravereaux and Jacod [1], one can find the study of the Malliavin operator on Wiener-Poisson space and application of it to stochastic differential equations. Both in these works, the authors have given differential operators on Wiener-Poisson space and have proved the integration by parts formulas. These formulation suffers some limitation on an intensity measure, that is, the intensity measure must have a smooth density. On the other hand, in the Malliavin calculus for Wiener functionals, Wiener chaos expansion of the space of square integrable Wiener functionals can be considered as a Fock space, and the differential operator is regarded as the annihilation operator on a Fock space. This sort of structure can be also found in the case of the space of square integrable functionals of Wiener-Poisson space, see [6]. Nualart and Vives [10], [11], and Picard [13] have studied the annihilation operator and its dual operator (the creation operator) on the space of square integrable functionals of a Poisson random measure. Picard [12] has also given a smoothness criterion by using the duality formula (see Theorem 2.1) for functionals of a Poisson random measure under the Condition 1 (see Section 2) on the intensity measure, and has studied the solution to some stochastic differential equation. This argument of Picard can be generalized for some Wiener-Poisson functionals, see [5]. The Condition 1 differs from that of [1], and allows us to take a intensity measure with some singularity. One can find some interesting examples satisfying Condition 1, for instance, stable processes and CGMY processes (see [3]). The purpose of this paper is to prove the asymptotic expansion theorem (done in the Wiener space by Watanabe [18]) for functionals of a Poisson random measure. By using the Malliavin operator which we mentioned above, Sakamoto and Yoshida [15] have studied asymptotic expansion formulas of some","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .
设P是对所有j∈[1,d−1]由可逆矩阵(a ij) di,j =1, dj = 0定义的PGL(d, C)的极大抛物子群。取PGL(d, C) /P型全纯抛物几何(M, exp， ω)。假设M是一个复射影流形。我们证明了:如果存在一个非常全纯映射f: CP 1−→M，则M对射影空间CP d−1是生物全纯的。
{"title":"On parabolic geometry of type PGL(d,C)/P","authors":"I. Biswas","doi":"10.1215/KJM/1250271316","DOIUrl":"https://doi.org/10.1215/KJM/1250271316","url":null,"abstract":"Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：