Equivalence Classes in the Weyl groups of type B_n

2006/07/09 by Thomas Pietraho, Pietraho, Thomas
Mathematics · #05E10 #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Representation Theory (math.RT) #math.CO #math.RT #msc:05E10 #msc:20C08

paper · pdf · doi:10.48550/arxiv.math/0607231

14 pages; Expanded introduction and references;

openalex publication_date 2006/07/09 · arxiv created 2007/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. 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.

Related

• Module structure of cells in unequal parameter Hecke algebras
• Left cells in type B_n with unequal parameters
• Seminormal representations of Weyl groups and Iwahori-Hecke algebras
• Hecke algebras with unequal parameters
• Open problems on Iwahori-Hecke algebras