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