On Seidel representation in quantum K-theory of Grassmannians

TL;DR

This paper provides a direct proof of Seidel representation in quantum K-theory for Grassmannians, offering new proofs and computational rules for quantum Schubert calculus.

Contribution

It introduces a concrete proof of Seidel representation in quantum K-theory and derives new computational tools for quantum Schubert calculus on Grassmannians.

Findings

Alternative proof of quantum Pieri rule by Buch and Mihalcea

Reduction of quantum structure constants to classical Littlewood-Richardson coefficients

Quantum Littlewood-Richardson rule for QK(Gr(3, n))

Abstract

We provide a direct proof of Seidel representation in the quantum K-theory QK(Gr(k, n)) by studying projected Gromov-Witten varieties concretely. As applications, we give an alternative proof of the K-theoretic quantum Pieri rule by Buch and Mihalcea, reduce certain quantum Schubert structure constants of higher degree to classical Littlewood-Richardson coefficients for K(Gr(k, n)), and provide a quantum Littlewood-Richardson rule for QK(Gr(3, n)).