Details

Autor(en) / Beteiligte

• Feng, Yongqi
• Opdam, Eric

Titel

On a uniqueness property of supercuspidal unipotent representations

Ist Teil von

• Advances in mathematics (New York. 1965), 2020-12, Vol.375, p.107406, Article 107406

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig [17]), is a rational function of q evaluated at q=q, the cardinality of the residue field. The irreducible factors of this rational function are q and cyclotomic polynomials. We prove that the formal degree of a supercuspidal unipotent representation determines its Lusztig-Langlands parameter, up to twisting by weakly unramified characters. For split exceptional groups this result follows from the work of M. Reeder [28], and for the remaining exceptional cases this is verified in [7]. In the present paper we treat the classical families. The main result of this article characterizes unramified Lusztig-Langlands parameters which support a cuspidal local system in terms of formal degrees. The result implies the uniqueness of so-called cuspidal spectral transfer morphisms (as introduced in [22]) between unipotent affine Hecke algebras (up to twisting by unramified characters). In [23] the essential uniqueness of arbitrary unipotent spectral transfer morphisms was reduced to the cuspidal case.