Acta Mathematica

Discrete series characters for affine Hecke algebras and their formal degrees

Eric Opdam and Maarten Solleveld

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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).

Article information

Acta Math., Volume 205, Number 1 (2010), 105-187.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20C08; Secondary 22D25
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.

affine Hecke algebra discrete series character formal dimension

2010 © Institut Mittag-Leffler


Opdam, Eric; Solleveld, Maarten. Discrete series characters for affine Hecke algebras and their formal degrees. Acta Math. 205 (2010), no. 1, 105--187. doi:10.1007/s11511-010-0052-9.

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