Cohomological integrality for weakly symmetric representations of reductive groups

2024/06/13 by Lucien Hennecart, Hennecart, Lucien · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.09218

openalex publication_date 2024/06/13 · openalex created_date 2024/06/15 · openalex updated_date 2026/08/03

Abstract

In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components indexed by some equivalence classes of cocharacters of a maximal torus. This decomposition enables the definition of new enumerative invariants associated with the stack, which we begin to explore.

Cited by

• The BPS decomposition theorem
• Cohomological Mackey formula for quotient stacks

Related

• Cohomological integrality for symmetric quotient stacks
• Dirac cohomology of minimal representations
• Cohomology of algebraic groups with coefficients in twisted representations
• Representations of Reductive Groups over Quotients of Local Rings
• Cohomological invariants of root stacks and admissible double coverings