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Knuth relations for the hyperoctahedral groups

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Abstract

C. Bonnafé, M. Geck, L. Iancu, and T. Lam have conjectured a description of Kazhdan-Lusztig cells in unequal parameter Hecke algebras of type B which is based on domino tableaux of arbitrary rank. In the integer case, this generalizes the work of D. Garfinkle. We adapt her methods and construct a family of operators which generate the equivalence classes on pairs of arbitrary rank domino tableaux described in the above conjecture.

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Correspondence to Thomas Pietraho.

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Pietraho, T. Knuth relations for the hyperoctahedral groups. J Algebr Comb 29, 509–535 (2009) doi:10.1007/s10801-008-0148-x

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Keywords

  • Unequal parameter Iwahori-Hecke algebra
  • Domino tableaux
  • Robinson-Schensted algorithm