1997/11/13 by Anatol N. Kirillov, Anatol N. KirilloV, Atsuo Kuniba +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Random Matrices and Applications #math.QA #q-alg
paper · pdf · doi:10.1016/s0550-3213(98)00351-4
published as Nucl. Phys. B529 [PM] (1998) 611-638 · AMS-LaTeX, 27 pages
arxiv created 1997/11/13 · openalex publication_date 1998/10/01 · arxiv updated 2011/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The spectral decomposition of the path space of the vertex model associated to the level l representation of the quantized affine algebra Uq(sln) 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 lΛk of sln and a generalization of the theorem.