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REPRESENTATION THEORY AND COMBINATORICS AND RELATED TOPICS

表示理论和组合学及相关主题

基本信息

批准号：
11640044
负责人：
KOIKE Kazuhiko
金额：
$ 2.24万
依托单位：
AOYAMA GAKUIN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
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

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640044/
关键词：
symmetric groups Weyl groups Hecke algebras dual pairs Spin groups Super Lie algebras algebras two-sided cells

项目摘要

Koike constructed all the irreducible representations of the Spin groups in the tensor spaces of the natural representations of the orthogonal groups and the fundamental Spin representation. This construction is a natural extension of the argument which is developed by H.Weyl in his famous book "The Classical Groups" and makes up the missing cases. Namely Koike considers the centralizer algebras of the Spin groups in the above tensor spaces (These algebras are natural analogs of the symmetric groups and Brauer's centralizer algebras in the classical cases.) and gives the explicit bases of the above algebras which are parameterized by the "extended Brauer diagrams". Koike also defines the subspaces of the above tensor spaces on which the symmetric group and the Spin group acts as the dual pair.In collaborated papers, Taniguchi extends the notion of a kind of the Molien series (it is a rational polynomial in one variable q.) to all the finite reflection groups, which was introduced by Kawanaka Noriaki (Osaka University) in case of the symmetric groups. Taniguchi and his collaborators give explicit formulas of those rational polynomials and reveal connections of the two-sided cells of the Iwahori Hecke algebras and those polynomials.Yamaguchi shows the representational background of the classical result of I.Schur which gives the characters of the irreducible projective representations of the symmetric groups. Namely based on Sergeev's duality of the twisted groups algebras of the hyperoctahedral groups and the Lie superalgebras, Yamaguchi defines immersions of the twisted groups algebras of the symmetric groups into the above twisted groups algebras and gives the subspaces, on which the twisted groups algebras of the symmetric groups and the Lie superalgebras act as the dual pair.

小池构建了所有的不可约表示的自旋群在张量空间的自然表示的正交群和基本的自旋表示。这种结构是H.Weyl在其著名著作《古典群》中提出的论点的自然延伸，并弥补了缺失的案例。即小池认为中心化代数的自旋群在上述张量空间（这些代数是自然类似的对称群和布劳尔的中心化代数在经典的情况下。并给出了由“扩展Brauer图”参数化的上述代数的显式基。小池还定义了上述张量空间的子空间，对称群和自旋群在其上充当对偶对。在合作论文中，谷口扩展了一种莫里安级数的概念（它是一个变量q的有理多项式）。Kawanaka Noriaki（大坂大学）在对称群的情况下引入的所有有限反射群。Taniguchi和他的合作者给出了这些有理多项式的显式公式，揭示了Iwahori Hecke代数的双边胞与这些多项式的联系，Yamaguchi给出了Schur给出对称群的不可约射影表示的特征的经典结果的代表性背景.即基于超八面体群的扭群代数与李超代数的Sergeev对偶，Yamaguchi定义了对称群的扭群代数浸入到上述扭群代数中，并给出了对称群的扭群代数与李超代数作为对偶对的子空间.