Casselman's basis of Iwahori vectors and the Bruhat order

2010/02/16 by Daniel Bump, Bump, Daniel, Maki Nakasuji +1
Mathematics · #20C08 #20F55 #22E50 #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:20C08 #msc:20F55 #msc:22E50

paper · pdf · doi:10.48550/arxiv.1002.2996

Added abstract to paper, one MSC-class, corrected typos and removed a word from the title

openalex publication_date 2010/02/16 · arxiv created 2010/02/18 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Casselman basis of Iwahori fixed vectors in a principal series representation of a p-adic group G is dual to the standard intertwining operators. To compute it one must compute a matrix m(u,v) indexed by pairs of Weyl group elements. This matrix is upper triangular with respect to the Bruhat order. In general this matrix is difficult to compute but it is shown that certain elements have a nice expression. This is also true of the inverse matrix to m(u,v). This leads to interesting conjectures regarding the Bruhat order.

Citations

• On some Bruhat decomposition and the structure of the Hecke rings of p -adic Chevalley groups

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