Cohomological Mackey formula for quotient stacks

2025/05/14 by Lucien Hennecart, Hennecart, Lucien
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.09483

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct a restriction morphism on the critical cohomology of an equivariant Landau-Ginzburg model associated to a representation of a reductive group equipped with an invariant function. We show a compatibility formula between the restriction and induction maps as a Mackey-type formula, thereby giving the critical cohomology the structure of a localized induction-restriction system.

Citations

• Intrinsic Donaldson-Thomas theory. I. Component lattices of stacks
• Cohomology of symmetric stacks
• Orthosymplectic modules of cohomological Hall algebras
• The Langlands formula and perverse sheaves
• Cohomological integrality for symmetric quotient stacks
• Decomposition theorem for good moduli morphisms
• Cohomological integrality for weakly symmetric representations of reductive groups
• Cohomological Hall algebras of quivers and Yangians
• Okounkov's conjecture via BPS Lie algebras
• Generators of the preprojective CoHA of a quiver
• BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories
• Geometric realisations of the unipotent enveloping algebra of a quiver
• Shuffle algebras for quivers and wheel conditions
• On cohomological Hall algebras of quivers : Yangians
• The integrality conjecture and the cohomology of preprojective stacks
• Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
• Generalized Springer Theory for D-modules on a Reductive Lie Algebra
• Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for 2-dimensional Calabi-Yau categories (with an appendix by Ben Davison)
• Donaldson-Thomas invariants versus intersection cohomology of quiver moduli
• Perverse Schobers
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Localization in equivariant intersection theory and the Bott residue formula

Related

• Recovering a cohomological Mackey Functor from its restriction to Sylow subgroups
• Some remarks on Mackey functors
• Computational proof of the Mackey formula for q > 2
• Matrix factorizations and Cohomological Field Theories
• Mackey functors and classical equivariant K-theory