Remarks on Fermionic Formula
Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi, Yasuhiko Yamada
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 Uq(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 Xn.
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