Combinatorial R matrices for a family of crystals : C(1)n and A(2)2n-1 cases
Abstract
The combinatorial R matrices are obtained for a family Bl of crystals for U'q(C(1)n) and U'q(A(2)2n-1), where Bl is the crystal of the irreducible module corresponding to the one-row Young diagram of length l. The isomorphism Bl Bk Bk Bl and the energy function are described explicitly in terms of a Cn-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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