Quantum K-Theory of Grassmannians and Non-Abelian Localization

Abstract

In the example of complex Grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the 𝑞-hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants, including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.