Affine Laumon spaces and iterated W-algebras

TL;DR

This paper introduces a family of vertex algebras linked to affine Laumon spaces, providing explicit formulas for their cohomology and proposing a new class called iterated W-algebras, with conjectures on their relationships.

Contribution

It constructs a new family of vertex algebras related to affine Laumon spaces and introduces iterated W-algebras via a novel quantum Hamiltonian reduction.

Findings

Explicit generating functions for Poincare polynomials of affine Laumon spaces.

Identification of vertex algebras with cohomology of these spaces.

Conjecture that these vertex algebras are subalgebras of iterated W-algebras.

Abstract

A family of vertex algebras whose universal Verma modules coincide with the cohomology of affine Laumon spaces is found. This result is based on an explicit expression for the generating function of Poincare polynomials of these spaces. There is a variant of quantum Hamiltonian reduction that realizes vertex algebras which we call iterated W-algebras and our main conjecture is that the vertex algebras associated to the affine Laumon spaces are subalgebras of iterated W-algebras.