Discrete series characters for affine Hecke algebras and their formal degrees

Details Discrete series characters for affine Hecke algebras and their formal degrees Discrete series characters for affine Hecke algebras and their formal degrees

2008-03-31

arxiv.org/abs/0804.0026v2

Acta Mathematica 205 (2010), 105-187

Mathematics

Representation Theory

68 pages, 5 figures. In the second version an appendix was added

Scientific paper

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) with arbitrary positive parameters and we prove an explicit product formula for their formal degrees (in all cases).

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