Remarks on Fermionic Formula

Abstract

Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the fermionic formulae associated with general non-twisted quantum affine algebra U_q(X^{(1)}_n) and discuss several aspects related to representation theories and combinatorics. They include crystal base theory, one dimensional sums, spinon character formulae, Q-system and combinatorial completeness of the string hypothesis for arbitrary X_n.

arXiv comment49 pages, no figures, LaTeX2e using package amsmath

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