Koszul duality in representation theory

表示论中的科祖尔对偶性

• 批准号: 124928406
• 负责人: Professor Dr. Wolfgang Soergel
• 金额: --
• 依托单位: Mathematisches Institut
• 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 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/124928406?language=en
• 关键词: Koszul; duality; representation; theory

The Koszul duality conjecture of the applicant, hopefully soon a theorem by Nadler and Ben-Zvi, conjectures a way to lift the local Langlands correspondence to the level of an equivalence of triangulated categories between roughly speaking the derived category of a category of representations and the equivariant derived category of the Langlands parameter space, more precisely it's version by Adams, Barbasch and Vogan. Our goal is to understand what the operations of tensoring with finite dimensional representation and induction correspond to on the the other side of this equivalence, i.e. in the equivariant derived category of the Langlands parameter space.

申请者的Koszul对偶猜想，希望很快能成为Nadler和Ben-Zvi的一个定理，它推测了一种方法，可以将局部朗兰兹对应提升到三角化范畴的等价水平，粗略地说，在表示范畴的派生范畴和朗兰兹参数空间的等变派生范畴之间，更准确地说，是Adams， Barbasch和Vogan的版本。我们的目标是理解有限维表示和归纳的张拉操作对应于这个等价的另一边，即在朗兰兹参数空间的等变派生范畴中。