Supercuspidal representations of \(SL_ n\) over a p-adic field: The tame case. (English) Zbl 0539.22014

Moy, Allen; Sally, Paul J. jun.

Duke Math. J. 51, 149-161 (1984).

The authors study the restriction of an irreducible supercuspidal representation of \(GL_ n(F)\) (F a p-adic field) to \(SL_ n(F)\) when n is prime to p, the residual characteristic of F. They are able to identify the irreducible components of the restricted representation if n and q-1 are also prime, where q is the order of the residue class field of F. When combined with earlier work of the reviewer and the first named author this yields a classification of the supercuspidal representations of \(SL_ n(F)\) in this case. In general they reduce the problem of determining the irreducible components to the analogous problem over the residue class field.

Reviewer: R.Howe

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

discrete series; irreducible supercuspidal representation

References:

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