Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} cases

Details Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} cases Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} cases

1999-09-14

arxiv.org/abs/math/9909068v2

Prog. Math. Phys. 191 "Physical Combinatorics" (2000) 105--139

Mathematics

Quantum Algebra

38 pages, latex2e, no figure

Scientific paper

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\otimes B_k \simeq B_k \otimes 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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