Level correspondence of $K$-theoretic $I$-function in Grassmann duality

TL;DR

This paper establishes a level correspondence phenomenon in Grassmann duality by proving q-Pochhammer identities and relating quasi-map K-theoretic I-functions between Grassmannians and their duals.

Contribution

It introduces the concept of level correspondence in Grassmann duality and derives relations between K-theoretic I-functions using new q-Pochhammer identities.

Findings

Identifies an interval of levels where I-functions coincide

Shows boundary levels where I-functions intertwine

Proves new q-Pochhammer symbol identities

Abstract

In this paper, we prove a class of nontrivial q-Pochhammer symbol identities with extra parameters by iterated residue method. Then we use these identities to find relations of the quasi-map $K$-theoretical $I$-functions with level structure between Grassmannian and its dual Grassmannian. Here we find an interval of levels within which two $I$-functions are the same, and on the boundary of that interval, two $I$-functions are intertwining with each other. We call this phenomenon level correspondence in Grassmann duality.