K-Theory of Hilbert Schemes as a Formal Quantum Field Theory

Abstract

We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute K-theoretical intersection theories on Hilbert schemes via a connection to Macdonald polynomials and vertex operators.

References in corpus (8)

• Seiberg-Witten prepotential from instanton counting
• Curve counting and instanton counting
• Macdonald operators and homological invariants of the colored Hopf link
• Hilbert schemes, Hecke algebras and the Calogero-Sutherland system
• Vertex Operators and Moduli Spaces of Sheaves
• Topological String Partition Functions as Equivariant Indices
• Rational Cherednik algebras and Hilbert schemes II: representations and sheaves
• On Quasimodularity of Some Equivariant Intersection Numbers on the Hilbert Schemes

Cited by in corpus (4)

• The virtual K-theory of Quot schemes of surfaces
• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions
• Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
• K-Theoretic Descendent Series for Hilbert Schemes of Points on Surfaces