Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels

Details Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels

1997-11-13

arxiv.org/abs/q-alg/9711009v1

Nucl. Phys. B529 [PM] (1998) 611-638

Mathematics

Quantum Algebra

AMS-LaTeX, 27 pages

Scientific paper

10.1016/S0550-3213(98)00351-4

The spectral decomposition of the path space of the vertex model associated to the level $l$ representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. The spectrum and its degeneracy are parametrized by skew Young diagrams and what we call nonmovable tableaux on them, respectively. As a result we obtain the characters for the degeneracy of the spectrum in terms of an alternating sum of skew Schur functions. Also studied are new combinatorial descriptions (spectral decomposition) of the Kostka numbers and the Kostka--Foulkes polynomials. As an application we give a new proof of Nakayashiki--Yamada's theorem about the branching functions of the level $l$ basic representation $l\Lambda_k$ of $\hat{sl}_n$ and a generalization of the theorem.

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