Kostant section, universal centralizer, and a modular derived Satake equivalence

2014/11/12 by Simon Riche, Riche, Simon
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1411.3112

v1: 27 pages; v2: minor reorganization; v3: 28 pages, minor additions; v4: 38 pages, title changed to reflect the addition of an application to a derived Satake equivalence

openalex publication_date 2014/11/12 · arxiv created 2015/05/19 · arxiv updated 2015/05/20 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28

Abstract

We prove analogues of fundamental results of Kostant on the universal centralizer of a connected reductive algebraic group for algebraically closed fields of positive characteristic (with mild assumptions), and for integral coefficients. As an application, we use these results to obtain a "mixed modular" analogue of the derived Satake equivalence of Bezrukavnikov-Finkelberg.

Citations

• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras

Related

• Some applications of the geometric Satake equivalence to modular representation theory
• Component groups of unipotent centralizers in good characteristic
• Centralisers of semi-simple elements are semidirect products
• Nilpotent centralizers and good filtrations
• The partial compactification of the universal centralizer