Difference L operators related to q-characters

Abstract

We introduce a factorized difference operator L(u) annihilated by the Frenkel-Reshetikhin screening operator for the quantum affine algebra U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental q-characters, and establish a number of formulas for their higher analogues. They include Jacobi-Trudi and Weyl type formulas, canceling tableau sums, Casorati determinant solution to the T-system, and so forth. Analogous operators for the orthogonal series U_q(B^{(1)}_n) and U_q(D^{(1)}_n) are also presented.

25 pages, LaTeX2e, no figure

References in corpus (3)

• Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
• Differential equations for general SU(n) Bethe ansatz systems
• Functional Relations in Stokes Multipliers and Solvable Models related to U_q(A^{(1)}_n)

Cited by in corpus (8)

• T-systems and Y-systems in integrable systems
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Paths, tableaux, and q-characters of quantum affine algebras: the C_n case
• Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Linear recurrence relations in $Q$-systems and difference $L$-operators
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system
• Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$