Casselman's basis of Iwahori vectors and the Bruhat order

Details Casselman's basis of Iwahori vectors and the Bruhat order Casselman's basis of Iwahori vectors and the Bruhat order

2010-02-16

arxiv.org/abs/1002.2996v2

Mathematics

Representation Theory

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

Scientific paper

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.

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