Cohomological integrality for weakly symmetric representations of reductive groups

TL;DR

This paper proves an integrality conjecture for quotient stacks from weakly symmetric reductive group representations, decomposing their cohomology and introducing new enumerative invariants.

Contribution

It establishes the integrality conjecture for these stacks and provides a cohomological decomposition framework that leads to novel enumerative invariants.

Findings

Cohomology decomposes into finite-dimensional components

New enumerative invariants are defined from the decomposition

Main result confirms the integrality conjecture

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.