Chevalley Restriction, Lie Algebra Cohomology, and Black Holes

Organizers

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker

Chi-Ming Chang 张其明

YMSC, Tsinghua University

Time & Venue

Monday, April 20, 3:30-4:30 pm

B627, Shuangqing Complex Building

Chevalley Restriction, Lie Algebra Cohomology, and Black Holes

This talk discusses several representation-theoretic questions arising from BPS operators in supersymmetric gauge theory and from black holes in holography. I will begin with the classical Chevalley restriction theorem and its extensions to commuting schemes and super-commuting schemes. For ordinary commuting schemes, many restriction results are known, while in the super case one finds explicit non-Cartan classes obstructing the naive analogue of Chevalley restriction. I will then explain how relative Lie algebra cohomology and the Loday-Quillen-Tsygan theorem enter the finite-rank problem, and how explicit fortuitous classes give counterexamples to the Loday-Feigin expectation. Finally, I will discuss recent evidence that after introducing a quantum deformation of the differential, the non-Cartan and fortuitous classes become linked, and a Langlands-duality between the cohomologies for Langlands-dual Lie algebras may be restored.