Weights uniquely determine simple modules for quasi-simply-connected affine Hecke algebras, and induction/restriction along isogenies preserve semisimplicity, Hermitian duals and unitarity.
Affine Hecke Algebras, Cyclotomic Hecke algebras and Clifford Theory
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Weights and characters for affine Hecke algebras
Weights uniquely determine simple modules for quasi-simply-connected affine Hecke algebras, and induction/restriction along isogenies preserve semisimplicity, Hermitian duals and unitarity.