Remarks on Fermionic Formula

1998/12/31 by Goro Hatayama, Atsuo Kuniba, Masato Okado +2 · 1 citation
Mathematics · Physics and Astronomy · #math.QA #hep-th #nlin.SI #solv-int #msc:81R10 #msc:81R50 #msc:82B23 #msc:05E15

paper · pdf

published as Contemporary Mathematics 248(1999) 243-291 · 49 pages, no figures, LaTeX2e using package amsmath

arxiv created 1999/07/30 · arxiv updated 2009/11/30

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.

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