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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 andnon-abelian correspondence. As a consequence, we generalize Givental-Lee'sresult to find the analogous "Toda operators" for the $I$-function withnontrivial level structures in the case of complete flag variety.

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