Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

TL;DR

This paper introduces factorized difference operators linked to twisted quantum affine algebras and constructs Casorati determinant solutions to the T-system, advancing the understanding of these algebraic structures.

Contribution

It presents new factorized difference operators for twisted quantum affine algebras and constructs Casorati determinant solutions to their T-systems.

Findings

Operators are annihilated by a screening operator.

Constructed Casorati determinant solutions to the T-system.

Established a basis of solutions for the difference equations.

Abstract

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).