Reconstruction of $g=1$ permutation equivariant quantum $K$-invariants

TL;DR

This paper extends the understanding of permutation-equivariant quantum K-invariants by establishing a genus one analog of Dijkgraaf-Witten's theorem, broadening the theoretical framework in quantum K-theory.

Contribution

It introduces a genus one analog of Dijkgraaf-Witten's theorem for permutation-equivariant quantum K-invariants, generalizing previous results.

Findings

Established a genus one Dijkgraaf-Witten analog in quantum K-theory

Generalized prior results to include $g=1$ invariants

Expanded the theoretical foundation of permutation-equivariant quantum K-invariants

Abstract

In this paper, we establish an analog of Dijkgraaf-Witten's theorem for $g=1$ invariants in permutation-equivariant quantum K-theory. This result generalizes the findings of \cite{Tang1} and \cite{Tang2}.