Action of Clifford algebra on the space of sequences of transfer operators

TL;DR

This paper establishes a connection between Clifford algebra modules and transfer matrices in quantum integrable spin chains, enabling the derivation of tau-functions from symmetric functions.

Contribution

It introduces a novel isomorphism linking Clifford algebra modules of transfer matrices to the boson space of symmetric functions, advancing the mathematical understanding of quantum integrable models.

Findings

Derived generating functions from quantum transfer matrices.

Constructed an isomorphism between Clifford modules and symmetric functions.

Connected tau-functions of transfer matrices to classical symmetric function tau-functions.

Abstract

We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Clifford algebra modules of sequences of transfer matrices and the boson space of symmetric functions. As an application, tau-functions of transfer matrices immediately arise from classical tau-functions of symmetric functions.