Hermitian symmetric modular category O

埃尔米特对称模类别 O

• 批准号: 219517071
• 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: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219517071?language=en
• 关键词: Hermitian; symmetric; modular; category

The case of a parabolic category O when the parabolic has an abelian unipotent radical, the so-called hermitian symmetric case, is special in that the Kazhdan-Lusztig-conjectures can be proven without using the decomposition theorem and the extensions between Verma modules are known. This gives hope that it should be possible to prove analogous statements in the modular case. Generalizing the modular Koszul duality recently established by the applicant in collaboration with Simon Riche and Geordie Williamson to a parabolic-singular duality, this should lead to new formulas for extensions of singular Weyl modules.

抛物范畴O当抛物线有交换单幂等根时，即所谓的厄米对称情形是特殊的，因为Kazhdan-Lusztig-猜想可以不用分解定理来证明，而且Verma模之间的扩张是已知的。这给了人们希望，在模块化的情况下，应该可以证明类似的陈述。将申请人最近与Simon Riche和Geordie Williamson合作建立的模Koszul对偶推广到抛物-奇异对偶，这应该会得到奇异Weyl模的扩张的新公式。