A computational criterion for the Kac conjecture

Abstract

We give a criterion for the Kac conjecture asserting that the free term of the polynomial counting the absolutely indecomposable representations of a quiver over a finite field of given dimension coincides with the corresponding root multiplicity of the associated Kac-Moody algebra. Our criterion suits very well for computer tests.

References in corpus (2)

• Mixed Hodge structures of configuration spaces
• Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform

Cited by in corpus (25)

• Motivic Donaldson-Thomas invariants and McKay correspondence
• On the noncommutative Donaldson-Thomas invariants arising from brane tilings
• Invariants of moduli spaces of stable sheaves on ruled surfaces
• Fermionic forms and quiver varieties
• Counting Higgs bundles and type A quiver bundles
• Intersection cohomology of moduli spaces of sheaves on surfaces
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Wall-crossing formulas for framed objects
• Motivic Donaldson-Thomas invariants and Kac conjecture
• On the number of stable quiver representations over finite fields
• A generalization of Kac polynomials and tensor product of representations of $G{L}_n({\mathbb{F}}_q)$
• On the multiplicities of the irreducible highest weight modules over Kac-Moody algebras
• Higgs bundles over P^1 and quiver representations
• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties
• DT invariants from vertex algebras
• Kac's conjecture from Nakajima quiver varieties
• Commuting matrices and volumes of linear stacks
• Motivic classes of Quot-schemes on surfaces
• Counting Representations of Quivers Respecting Nilpotent Relations over Finite Fields
• On Numbers of Tuples of Nilpotent Matrices over Finite Fields under Simultaneous Conjugation
• Cohomology of non-generic character stacks
• $e$-polynomials of character varieties
• Tensor products of unipotent characters of general linear groups over finite fields
• Stringy motives of symmetric products
• Poincare polynomials of moduli spaces of stable bundles over curves