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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn023, 41 pages, doi:10.1093/imrn/rnn023 published on April 11, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Induced Discrete Series Representations for Hecke Algebras of Types Formula and Formula

K. Slooten

Department of Mathematics, Utrecht University, Budapestlaan 6, P.O. Box 80010, 3508 TA Utrecht, The Netherlands

Correspondence: Correspondence to be sent to: slooten{at}math.uu.nl

Recently, Delorme and Opdam [7] 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 Formula or Formula , and the induced discrete series representation has positive central character. We show that the R-group of such an induced representation is isomorphic to Formula , and that the representation decomposes multiplicity-free into Formula irreducible summands. The number d is calculated by combinatorial means.


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