Open Access
2010 Discrete series characters for affine Hecke algebras and their formal degrees
Eric Opdam, Maarten Solleveld
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Acta Math. 205(1): 105-187 (2010). DOI: 10.1007/s11511-010-0052-9


We introduce the generic central character of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types ${E_{n}^{(1)}}$ , n=6, 7, 8) with arbitrary positive parameters and we prove an explicit product formula for their formal degrees (in all cases).


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Eric Opdam. Maarten Solleveld. "Discrete series characters for affine Hecke algebras and their formal degrees." Acta Math. 205 (1) 105 - 187, 2010.


Received: 18 June 2008; Revised: 31 March 2009; Published: 2010
First available in Project Euclid: 31 January 2017

zbMATH: 1214.20008
MathSciNet: MR2736154
Digital Object Identifier: 10.1007/s11511-010-0052-9

Primary: 20C08; Secondary 22D25
Secondary: 43A30

Keywords: affine Hecke algebra , discrete series character , formal dimension

Rights: 2010 © Institut Mittag-Leffler

Vol.205 • No. 1 • 2010
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