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Discrete series characters for affine Hecke algebras and their formal degrees

Eric Opdam Korteweg de Vries Institute for Mathematics, University of Amsterdam Maarten Solleveld Mathematisches Institut, Universität Göttingen

TBD mathscidoc:1701.332019

Acta Mathematica, 205, (1), 105-187, 2008.6
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).
affine Hecke algebra; discrete series character; formal dimension
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@inproceedings{eric2008discrete,
  title={Discrete series characters for affine Hecke algebras and their formal degrees},
  author={Eric Opdam, and Maarten Solleveld},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355385942728},
  booktitle={Acta Mathematica},
  volume={205},
  number={1},
  pages={105-187},
  year={2008},
}
Eric Opdam, and Maarten Solleveld. Discrete series characters for affine Hecke algebras and their formal degrees. 2008. Vol. 205. In Acta Mathematica. pp.105-187. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355385942728.
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