PBW-filtration of representations, degenerate flag varieties and polytopes

PBW 过滤表征、简并标记变体和多胞体

• 批准号: 219429273
• 负责人: Professor Dr. Peter Littelmann
• 金额: --
• 依托单位: Abteilung Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219429273?language=en
• 关键词: PBW; filtration; representations; degenerate; flag

The project is part of a long term program to better understand the geometric, algebraic and combinatorial aspects of the PBW-filtration of a representation. Let g be a simple Lie algebra and let n- be the nilpotent radical of an opposite Borel subalgebra. The PBW-filtration of U(n-) induces a filtration on a finite dimensional irreducible representation Vλ, denote by Vλa the associated graded space. This construction leads naturally to an algebraic group Ga, which can be viewed as a degenerate version of the original group G with Lie algebra g. The group acts on Vλa, and, guided by the embedding of a flag variety Fλ _ P(Vλ), denote by Fλa the closure of the Ga-orbit through the image of highest weight line in P(Vλa).Geometric, algebraic and combinatorial aspects of this construction have been investigated for G = SLn and Sp2m in a series of papers by E. Feigin, M. Finkelberg, G. Fourier and the PI. The aim of this project is to generalize the results to other types as well as to link the newly developed methods and tools to other known constructions in representation theory like crystal bases and generalized Gelfand-Tsetlin patterns.

该项目是一个长期计划的一部分，以更好地了解几何，代数和组合方面的PBW过滤的表示。设g是单李代数，n-是一个相反的Borel子代数的幂零根. U（n-）的PBW-滤子在有限维不可约表示Vλ上导出一个滤子，Vλ表示为相应的分次空间。这种构造自然地导致一个代数群Ga，它可以被看作是具有李代数g的原群G的退化版本。这个群作用于Vλa上，在嵌入一个标志簇Fλ P（Vλ）的引导下，用Fλa表示通过P（Vλa）中最高权线象的Ga轨道的闭包. Feigin，M.芬克尔伯格，G。傅立叶和PI该项目的目的是将结果推广到其他类型，并将新开发的方法和工具与表示论中的其他已知结构（如晶体基和广义Gelfand-Tsetlin模式）联系起来。