Equivalence Classes in the Weyl groups of type $B_n$

Details Equivalence Classes in the Weyl groups of type $B_n$ Equivalence Classes in the Weyl groups of type $B_n$

2006-07-09

arxiv.org/abs/math/0607231v2

Mathematics

Combinatorics

14 pages; Expanded introduction and references;

Scientific paper

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 $r$. For $r=0$, the classes in the first family coincide with left cells corresponding to the equal parameter Iwahori-Hecke algebra. When $r$ is sufficiently large, the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters. 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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