Affine Laumon spaces and 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.

arXiv comment32 pages

References in corpus (12)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• Quantum Reduction for Affine Superalgebras
• A & B model approaches to surface operators and Toda theories
• Instanton counting with a surface operator and the chain-saw quiver
• Webs of W-algebras
• Trialities of $\mathcal{W}$-algebras
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• S-duality for the large $N=4$ superconformal algebra
• Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
• Affine Super Yangians and Rectangular $W$-superalgebras
• W-algebras and surface operators in N=2 gauge theories

Cited by in corpus (1)

• On the structure of W-algebras in type A