Cohomological integrality for weakly symmetric representations of reductive groups
arXiv:2406.09218 · doi:10.1017/S1474748025101357
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.
v6: 28 pages, accepted version; v5: 27pages. Many improvements following feedback. The main result now holds for weakly symmetric representations. Title adapted; v4: Abstract and introduction rewritten and exposition improved; v3: 24 pages, corrected Lemma 4.5, added Proposition 1.4; v2: fixed example section and proof of finite dimensionality; v1:22 pages, comments very welcome