# Reducibility of induced discrete series representations for affine Hecke algebras of type B

Source: [Reducibility of induced discrete series representations for affine Hecke algebras of type B](<https://www.sota2.com/research/paper/68fa4d3c1e209131ce952ed3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:12:34.863Z

Authors: K. Slooten

Published: 2005-11-08T15:43:36.000Z

## Abstract

Recently Delorme and Opdam have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series representation with real central character. We calculate the R-group of such an induced representation, and show that it decomposes multiplicity free into 2^d irreducible summands. The power d can be calculated combinatorially.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0511206>)

[PDF](<https://arxiv.org/pdf/math/0511206.pdf>)