Higher Schur-Weyl dualities and gradings

更高的 Schur-Weyl 对偶性和分级

• 批准号: 124909482
• 负责人: Professorin Dr. Catharina Stroppel
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/124909482?language=en
• 关键词: Higher; Schur; Weyl; dualities; gradings

The objective of the proposed project is a construction of graded versions of a family of algebras which arise, apart from representation theory, in invariant theory, topology and statistical mechanics. The focus is on the cyclotomic Wenzl algebras with the ultimate goal of a graded representation theory for nonsemisimple Brauer algebras. The approach is a type BCD analogue of higher Schur-Weyl duality; a newly developed method with big impact on the modular representation theory of the symmetric group, higher representation theory and categorification. While some of the techniques needed are already established in the case of the general linear Lie algebra, many of these fail when moving away from the type A setup, and we focus on developing suitable substitutes. The most fundamental one is a construction of quiver Hecke (KLR) algebras for cyclotomicWenzl algebras, both combinatorially as well as geometrically. As an application we expect to obtain character formulas and combinatorial models for tensor product decompositions of rational representations for Lie super groups, in particular in the ortho-symplectic cases. Related topics: Lie (super)algebras, quiver Hecke algebras, Deligne's category Rep GL(δ), twisted Yangians, perverse sheaves on isotropic Grassmannians.

该项目的目的是建立一个分级版本的家庭代数出现，除了表示理论，在不变理论，拓扑和统计力学。重点是分圆Wenzl代数与非半单Brauer代数的分级表示理论的最终目标。该方法是高阶Schur-Weyl对偶的BCD型模拟;一种新开发的方法，对对称群的模表示理论、高阶表示理论和范畴化有很大影响。虽然在一般线性李代数的情况下已经建立了一些所需的技术，但当远离A型设置时，其中许多技术都失败了，我们专注于开发合适的替代品。其中最基本的一个是分圆Wenzl代数的KLR代数的构造，无论是组合还是几何。作为一个应用，我们期望得到的特征公式和组合模型的张量积分解的合理表示李超群，特别是在正交辛的情况下。相关主题：Lie（super）代数，Lie Hecke代数，Deligne范畴Rep GL（δ），扭曲Yangians，迷向Grassmannian上的反常层。