K-Theoretic $I$-function of $V//_{\theta} \mathbf{G}$ and Application

TL;DR

This paper computes the K-theoretic I-function with level structure for GIT quotients of vector spaces, generalizing previous results and establishing Toda operators for complete flag varieties.

Contribution

It introduces a method to compute K-theoretic I-functions with level structure using abelian and non-abelian correspondence, extending known results to new cases.

Findings

Derived explicit formulas for K-theoretic I-functions with level structure.

Generalized Givental-Lee's results to include nontrivial level structures.

Established Toda operators for complete flag varieties.

Abstract

In this paper, we compute K-theoretic $I$-function with level structure (defined by quasi-map theory) of GIT-quotient of a vector space via abelian and non-abelian correspondence. As a consequence, we generalize Givental-Lee's result to find the analogous "Toda operators" for the $I$-function with nontrivial level structures in the case of complete flag variety.