Combinatorial R Matrices for a Family of Crystals: C n (1) and A 2n-1 (2) Cases

  • Hatayama G
  • Kuniba A
  • Okado M
  • et al.
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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\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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Hatayama, G., Kuniba, A., Okado, M., & Takagi, T. (2000). Combinatorial R Matrices for a Family of Crystals: C n (1) and A 2n-1 (2) Cases. In Physical Combinatorics (pp. 105–139). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-1378-9_3

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