Quantum K-theory of grassmannians and non-abelian localization

TL;DR

This paper explores advanced computational techniques for genus-0 K-theoretic Gromov-Witten invariants of complex grassmannians and related varieties, integrating hypergeometric series, difference operators, and mirror symmetry concepts.

Contribution

It introduces explicit reconstruction methods for K-theoretic invariants using finite-difference operators and develops the role of q-hypergeometric series and Jackson integrals in this context.

Findings

Explicit reconstruction of invariants achieved

Connection between q-hypergeometric series and mirror symmetry established

New techniques for twisted GW-invariants and level structures introduced

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.