Quantum $\mathrm{K}$-Theory of Grassmannians and Non-Abelian Localization

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-$0$ $\mathrm{K}$-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 $\mathrm{K}$-theoretic mirrors.