Permutation-equivariant quantum K-theory IV. $D_q$-modules

Abstract

In Part II, we saw how genus-0 permutation-equivariant quantum K-theory of a manifold with isolated fixed points of a torus action can be reduced via fixed point localization to permutation-equivariant quantum K-theory of the point. In Part III, we gave a complete description of genus-0 permutation-equivariant quantum K-theory of the point by means of adelic characterization. Here we apply the adelic characterization to introduce the action on this theory of a certain group of $q$-difference operators. This action will enable us to prove that toric $q$-hypergeometric functions represent K-theoretic GW-invariants of toric manifolds.

arXiv comment8 pages

References in corpus (1)

• The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory

Cited by in corpus (3)

• 3d Mirror Symmetry and Quantum $K$-theory of Hypertoric Varieties
• Quantum K-theory of grassmannians and non-abelian localization
• $K$-theoretic quasimap wall-crossing