Combinatorial R matrices for a family of crystals : C⁽¹⁾_n and A⁽²⁾_2n-1 cases

1999/09/16 by Goro Hatayama, Atsuo Kuniba, Masato Okado +1
Mathematics · Physics and Astronomy · #math.QA #nlin.SI #solv-int #msc:81R10 #msc:81R50

paper · pdf

published as Prog. Math. Phys. 191 "Physical Combinatorics" (2000) 105--139 · 38 pages, latex2e, no figure

arxiv created 1999/09/16 · arxiv updated 2009/11/30

Abstract

The combinatorial R matrices are obtained for a family B_l of crystals for U'_q(C⁽¹⁾_n) and U'_q(A⁽²⁾_2n-1), where B_l is the crystal of the irreducible module corresponding to the one-row Young diagram of length l. The isomorphism B_l⊗ B_k ≃ B_k ⊗ B_l and the energy function are described explicitly in terms of a C_n-analogue of the Robinson-Schensted-Knuth type insertion algorithm. As an application a C⁽¹⁾_n-analogue of the Kostka polynomials is calculated for several cases.

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