6 citations · 13 across the 17 of their papers we have counts for
17 papers
Commutativity of nilpotent cohomological Hall algebras of
Lucien Hennecart
In this paper, we prove that both the seminilpotent and the fully nilpotent CoHAs of are commutative. This result is in strong contrast with the CoHA of $\mathbf{A}^…
Hecke operators on symplectic surfaces and -independence
Ben Davison, Lucien Hennecart, Tasuki Kinjo +2
We prove Toda's chi-independence conjecture for the BPS cohomology of moduli spaces of one-dimensional sheaves on quasi-projective symplectic surfaces, relative to the Chow variety…
The Deligne-Simpson problem via 2-Calabi-Yau categories
Lucien Hennecart
We provide a short proof of the necessity of Crawley-Boevey's condition in his solution to the Deligne-Simpson problem. The proof relies on the local neighbourhood theorem for -…
Degenerations of CoHAs of 2-Calabi-Yau categories
Lucien Hennecart, Shivang Jindal
By work of Davison and Meinhardt, the cohomological Hall algebra of a symmetric quiver with potential admits a geometrically defined filtration (the perverse filtration) whose asso…
The BPS decomposition theorem
Lucien Hennecart, Tasuki Kinjo
We prove the BPS decomposition theorem (a.k.a. cohomological integrality theorem) decomposing the cohomology of smooth symmetric stacks into the Weyl-invariant part of the cohomolo…
Cohomological Mackey formula for quotient stacks
Lucien Hennecart
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 w…
Cohomological integrality for symmetric quotient stacks
Lucien Hennecart
In this paper, we establish the sheafified version of the cohomological integrality conjecture for stacks obtained as a quotient of a smooth affine symmetric algebraic variety by a…
Cohomological integrality for weakly symmetric representations of reductive groups
Lucien Hennecart
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…
Nonabelian Hodge isomorphisms for stacks and cohomological Hall algebras
Lucien Hennecart
In this paper, we complete the nonabelian Hodge theory (NAHT) triangle of isomorphisms for stacks between the Borel-Moore homologies of the Dolbeault, Betti, and de Rham moduli sta…
BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories
Ben Davison, Lucien Hennecart, Sebastian Schlegel Mejia
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic…
BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks
Ben Davison, Lucien Hennecart, Sebastian Schlegel Mejia
We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories of homological dimension at most two, and a sheaf-theoretic…
Geometric realisations of the unipotent enveloping algebra of a quiver
Lucien Hennecart
We compare and generalise the various geometric constructions (due to Ringel, Lusztig, Schofield, Bozec, Davison...) of the unipotent generalised Kac-Moody algebra associated with…
A Quiver Analogue of Higman's Conjecture
Lucien Hennecart, Nikolai Perry
An unresolved conjecture by Graham Higman states that for all the number of conjugacy classes of the group of unitriangular matrices with entries in the fini…
Perverse sheaves with nilpotent singular support on the stack of coherent sheaves on an elliptic curve
Lucien Hennecart
We define a stratification of the moduli stack of coherent sheaves on an elliptic curve which allows us (1) to give an explicit description of the irreducible components of the glo…
Microlocal characterization of Lusztig sheaves for affine quivers and -loops quivers
Lucien Hennecart
We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lu…
Asymptotic behaviour of Kac polynomials
Lucien Hennecart
We conjecture a formula supported by computations for the valuation of Kac polynomials of a quiver, which only depends on the number of loops at each vertex. We prove a convergence…
Isotropic cuspidal functions in the Hall algebra of a quiver
Lucien Hennecart
From the structure of the category of representations of an affine cycle-free quiver, we determine an explicit linear form on the space of regular cuspidal functions over a finite…