Showing 1 - 3 of 3 Items
Equivalence classes in the Weyl groups of type Bn
Date: 2008-04-01
Creator: Thomas Pietraho
Access: Open access
- 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. © 2007 Springer Science+Business Media, LLC.
Knuth relations for the hyperoctahedral groups
Date: 2009-06-01
Creator: Thomas Pietraho
Access: Open access
- 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. © 2008 Springer Science+Business Media, LLC.
Cells and constructible representations in type B
Date: 2008-10-13
Creator: Thomas Pietraho
Access: Open access
- We examine the partition of a finite Coxeter group of type B into cells determined by a weight function L. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with conjectured combinatorial descriptions of cells.