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Journal of Lie Theory 29 (2019), No. 4, 901--926
Copyright Heldermann Verlag 2019

A Note on The Spectral Transfer Morphism for Affine Hecke Algebras

Yongqi Feng
Institute for Mathematics, Astrophysics, and Particle Physics, Radboud Universiteit, Nijmegen, The Netherlands

Opdam introduced the notion of spectral transfer morphisms of affine Hecke algebras to study the formal degree of a unipotent discrete series representation. Based on the uniqueness property of supercuspidal unipotent representations established by Opdam and the author, Opdam proved that unipotent discrete series representations of classical groups can be classified by the associated formal degrees, in the same spirit as Reeder's result for split exceptional adjoint groups.
The present paper aims at verifying that three specific families of finite maps of algebraic tori are spectral transfer morphisms. These spectral transfer morphisms are used in the proof of Opdam's result mentioned above.

Keywords: Affine Hecke algebra, unipotent representation, discrete series representation, formal degree, spectral transfer morphism.

MSC: 20G25, 22E50

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