Cohomological integrality for weakly symmetric representations of reductive groups
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.
Keywords
Cite
@article{arxiv.2406.09218,
title = {Cohomological integrality for weakly symmetric representations of reductive groups},
author = {Lucien Hennecart},
journal= {arXiv preprint arXiv:2406.09218},
year = {2026}
}
Comments
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