Remarks on Fermionic Formula

Details Remarks on Fermionic Formula Remarks on Fermionic Formula

1998-12-03

arxiv.org/abs/math/9812022v3

Contemporary Mathematics 248(1999) 243-291

Mathematics

Quantum Algebra

49 pages, no figures, LaTeX2e using package amsmath

Scientific paper

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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