Pieri rules, vertex operators and Baxter Q-matrix

TL;DR

This paper connects Pieri rules, vertex operators, and Baxter Q-matrices to integrable models like the q-boson and Toda chain, revealing new algebraic structures and scalar product formulas.

Contribution

It introduces a novel approach using Pieri rules to recover and analyze the q-boson model and its relation to the relativistic Toda chain via vertex operators and dualities.

Findings

q-boson model is equivalent to a discretized relativistic Toda chain

Scalar product of higher spin XXZ wave functions expressed with Gaudin determinant

Identification of transfer matrix and Baxter Q-matrix with half vertex operators

Abstract

We use the Pieri rules to recover the q-boson model and show it is equivalent to a discretized version of the relativistic Toda chain. We identify its semi infinite transfer matrix and the corresponding Baxter Q-matrix with half vertex operators related by an {\omega}-duality transformation. We observe that the scalar product of two higher spin XXZ wave functions can be expressed with a Gaudin determinant.