Tridiagonal pairs of $q$-Racah type, the Bockting operator $\psi$, and $L$-operators for $U_q(L({\mathfrak{sl}}_2))$

TL;DR

This paper characterizes the Bockting operator for a specific class of tridiagonal pairs using an $L$-operator from the quantum loop algebra, advancing understanding of their algebraic structure.

Contribution

It introduces a new description of the Bockting operator for $q$-Racah type tridiagonal pairs via $L$-operators in quantum loop algebra.

Findings

Explicit expression for the Bockting operator $\psi$ in terms of $L$-operators.

Connection established between tridiagonal pairs and quantum loop algebra representations.

Enhanced algebraic framework for studying $q$-Racah type structures.

Abstract

We describe the Bockting operator $\psi$ for a tridiagonal pair of $q$-Racah type, in terms of a certain $L$-operator for the quantum loop algebra $U_q(L({\mathfrak {sl}}_2))$.