New relations in the algebra of the Baxter Q-operators

TL;DR

This paper explores new algebraic structures arising from the Baxter Q-operators in the six-vertex model, especially at roots of unity, revealing novel relations in the algebra of monodromy matrices.

Contribution

It introduces a new algebraic framework generated by L-operators and Q-operators for cyclic representations at roots of unity.

Findings

Q-operator represented as trace of tensor product of L-operators

New algebraic relations among Q-operators and L-operators

Enhanced understanding of the algebraic structure at roots of unity

Abstract

We consider irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model. In roots of unity the Baxter Q-operator can be represented as a trace of a tensor product of L-operators corresponding to one of these cyclic representations and satisfies the TQ-equation. We find a new algebraic structure generated by these L-operators and, as a consequence, by the Q-operators.