Sur les représentations non ramifiées des groupes réductifs p- adiques; l’exemple de GSp(4). (On the non-ramified representations of p- adic reductive groups; the example GSp(4)). (French) Zbl 0662.22011

Rodier, François

Bull. Soc. Math. Fr. 116, No. 1, 15-42 (1988); corrigendum ibid. 134, No. 3, 447-449 (2006).

The main aim of the paper is to describe irreducible non-ramified representations of split reductive groups over local fields. The author’s approach is based on Macdonald’s formulas for spherical functions [I. G. Macdonald, Spherical functions on a group of p-adic type (Publ. Ramanujan Inst. 2, 1971; Zbl 0302.43018)]. As an example the author studies such representations for the group \(GSp_ 4\). He describes all non-ramified representations, and studies some of their properties (the existence of the Whittaker model, unitarity, etc.). Some of these properties are studied also for non-ramified representations of arbitrary split groups.

Reviewer: S.I.Gel’fand

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

irreducible non-ramified representations; split reductive groups; local fields; spherical functions

Citations:

Zbl 0302.43018

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