Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case

Abstract

We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the numbers which formally count the off-diagonal solutions of the U_q(X^{(1)}_n) Bethe equation at q=0. The series are conjectured to be the X_n-character of a certain family of irreducible finite-dimensional U_q(X^{(1)}_n) -modules which we call the KR (Kirillov-Reshetikhin) modules. Under the above conjecture, these coefficients give a formula of the weight multiplicities of the tensor products of the KR modules, which is also interpreted as the formal completeness of the XXZ-type Bethe vectors.

32 pages, AMS-LaTeX; Typos corrected. Proof of Proposition 5.10 is simplified

References in corpus (4)

• The q-characters of representations of quantum affine algebras and deformations of W-algebras
• Drinfeld Functor and Finite-Dimensional Representations of Yangian
• Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case
• On the fermionc formula and the Kirillov-Reshetikhin conjecture

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• Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case
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