Abstract
We consider two families of equivalence classes in the Weyl groups of type B n which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by a non-negative integer r. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra when r=0; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters when r is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure of left cells for remaining choices of the Iwahori-Hecke algebra parameters.
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Pietraho, T. Equivalence classes in the Weyl groups of type B n . J Algebr Comb 27, 247–262 (2008). https://doi.org/10.1007/s10801-007-0085-0
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DOI: https://doi.org/10.1007/s10801-007-0085-0