Study of parity sheaves arising from graded Lie algebra

2020/07/24 by Tamanna Chatterjee, Chatterjee, Tamanna
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2007.12638

Abstract

Let G be a complex, connected, reductive, algebraic group, and χ:ℂ^× → G be a fixed cocharacter that defines a grading on \mathfrakg, the Lie algebra of G. Let G₀ be the centralizer of χ(ℂ^×). In this paper, we study G₀-equivariant parity sheaves on \mathfrakg_n, under some assumptions on the field \Bbbk and the group G. The assumption on G holds for GL_n and for any G, it recovers results of Lusztig in characteristic 0. The main result is that every parity sheaf occurs as a direct summand of the parabolic induction of some cuspidal pair.

Related

• A Note on primitive pairs for graded Lie algebras
• Equivariant sheaves for classical groups acting on Grassmannians
• Parabolic induction and perverse sheaves on h/W
• Z/m-graded Lie algebras and perverse sheaves, II
• Generalised Springer correspondence for Z/m-graded Lie algebras