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

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}).

💡 Research Summary

The paper introduces a family of 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})) and (U_q(D^{(3)}{4})). Each operator is built as a product of elementary factors of the form ((1 - Y_i(u) D^{\pm1})), where (Y_i(u)) are the usual (Y)-functions (spectral parameters) and (D) denotes the shift operator acting as ((Df)(u)=f(u+1)). The factorized form reflects the underlying Dynkin diagram and the twist, and it makes the algebraic structure of the operators transparent.

A central result is that every (L(u)) is annihilated by the corresponding screening operators (S_i). Explicitly, (