DT invariants and vertex algebras

Abstract: Cohomological Hall algebras (CoHAs) can be understood as a mathematical incarnation of algebras of BPS states in string theory. Their Poincare series can be used to determine DT invariants of the corresponding categories. For a symmetric quiver Q, the corresponding CoHA is commutative and I will explain how its dual can be naturally equipped with a structure of a vertex bialgebra. It can also be identified with 1) the universal enveloping algebra of some Lie algebra, 2) the universal enveloping vertex algebra of some vertex Lie algebra, 3) the principal free vertex algebra embedded into some lattice vertex algebra. This identification leads to a new proof of the positivity of DT invariants. It also allows one to interpret duals of CoHA modules, arising from moduli spaces of stable framed representations, as certain subspaces of principal free vertex algebras.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar