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Equivalence classes in the Weyl groups of type Bn

By Thomas Pietraho

Abstract

Abstract. We consider two families of equivalence classes in the Weyl groups of type Bn 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. 1

Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.234.7320
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