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Representation theory of algebraic groups through algebraic analysis

通过代数分析的代数群表示论

基本信息

批准号：
11440009
负责人：
TANISAKI Toshiyuki
金额：
$ 5.82万
依托单位：
Hiroshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

1. Highest weight modules over Kac-Moody Lie algebrasKashiwara and Tanisaki tried to determine characters of irreducible modules over affine Lie algebras with critical highest weights. In particular, they considered relations of representations of affine Lie algebras with D-modules on the semi-infinite flag manifold. Through the investigation they noticed that the behavior of the equivariant line bundles is quite different from those on the ordinary flag manifold.2. Flag manifold for quantum groupsTanisaki constructed generalized flag manifold corresponding to general parabolic subgroups. The treatment of the unipotent radical is more delicate than the ordinary case. Besides Morita and Tanisaki tried to find a good formulation for the sheaf cohomologies and D-modules on the quantized flag manifold from the view point of non-commutative schemes.3. Representations of toroidal Lie algebrasSaito constructed certain representations of toroidal Lie algebras usig Boson. He also investigated the automorphisms of the toroidal Lie algebras and found a connection with the moudular groups.4. Representations of quantum groups over Laurent polynimial ringsKaneda investigated representations of quantum groups over the Laurent polynimial rings, and have proved a version of a theorem of Kempf.5. Solvable gamesKawanaka found a generalization of Sato's game, and investigated on it from the view point of representation theory.6..Representations of comples reflection groups and their Hecke algebrasShoji tried to extend the Frobenius formua for the Hecke algebra of type A to the Hecke algebras for complex reflection groups, and succeed in it in the case of Ariki-Koike algebra.

1. Kac-Moody李代数上的最高权模Kashiwara和Tanisaki试图确定仿射李代数上具有临界最高权的不可约模的特征标。特别是，他们考虑了半无限旗流形上仿射李代数与D-模的表示关系。通过研究，他们注意到等变线丛的行为与普通旗流形上的行为有很大的不同.量子群的旗流形Tanisaki构造了对应于一般抛物子群的广义旗流形。幂幺根式的处理比一般情况更微妙。此外，Morita和Tanisaki试图从非交换模式的角度来寻找量子化旗流形上的层、上同调和D-模的一个很好的表述. Tooral李代数的表示Saito利用玻色子构造了Tooral李代数的某些表示。他还调查了自同构的环形李代数，并发现了一个连接与模群。4.表示的量子群在劳伦多项式环Kaneda调查表示的量子群在劳伦多项式环，并证明了一个版本的定理肯普夫。5。可解对策川中找到了佐藤对策的一个推广，并从表示论的角度对其进行了研究。Shoji试图将A型Hecke代数的Frobenius公式推广到复反射群的Hecke代数，并在Ariki-Koike代数的情况下取得了成功。