×

Tamely ramified supercuspidal representations of classical groups. I: Filtrations. (English) Zbl 0756.20006

Let \(G\) be a classical group defined over a local non-archimedean field \(k\). Let \(T\) be a tamely ramified compact maximal torus of \(G\). In the reviewed paper the author gives a construction of a parahoric subgroup \(P\) of \(G\), together with a remarkable filtration of \(P\) by normal open subgroups of \(P\) such that \(T\subset P\) and such that the family of these subgroups reflects the arithmetic of a prespecified ramified piece of \(T\). This is illustrated with some examples in small groups, in particular \(Sp_ 4\). This construction is proposed to be applied in the second part of this work to construct irreducible supercuspidal representations of \(G\) associated to \(T\) (excluding \(G\) over quaternion algebras).

MSC:

20G25 Linear algebraic groups over local fields and their integers
20G05 Representation theory for linear algebraic groups
22E50 Representations of Lie and linear algebraic groups over local fields
11E57 Classical groups
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] C. BUSHNELL , Hereditary Orders, Gauss Sums and Supercuspidal Representations of GLn (J. Reine Angew. Math., Vol. 375/376, 1987 , pp. 184-210). MR 88e:22024 | Zbl 0601.12025 · Zbl 0601.12025 · doi:10.1515/crll.1987.375-376.184
[2] C. BUSHNELL and A. FRÖHLICH , Non Abelian Congruence Gauss Sums and p-adic Simple Algebras (Proc. London Math. Soc., Vol. 50, 1985 , pp. 207-264). Zbl 0558.12007 · Zbl 0558.12007 · doi:10.1112/plms/s3-50.2.207
[3] F. BRUHAT and J. TITS , Groupes Réductifs sur un corps local II. Schémas en groupes... (Publ. Math. Inst. Hautes Études Sc., Vol. 60, 1984 , pp. 5-184). Numdam | Zbl 0597.14041 · Zbl 0597.14041 · doi:10.1007/BF02700560
[4] F. BRUHAT and J. TITS , Schémas en Groupes et Immeubles des Groupes Classiques sur un Corps Local (Bull. Soc. Math. France, Vol. 112, 1984 , pp. 259-301). Numdam | MR 86i:20064 | Zbl 0565.14028 · Zbl 0565.14028
[5] L. MORRIS , Some Tamely Ramified Supercuspidal Representations of Symplectic Groups (in press, Proc. London Math. Soc., Vol. 63, 1991 ). MR 92i:22017 | Zbl 0746.22013 · Zbl 0746.22013 · doi:10.1112/plms/s3-63.3.519
[6] L. MORRIS , P-cuspidal Representations (Proc. London Math. Soc., Vol. 57, 1988 , pp. 329-356). MR 89j:22038 | Zbl 0663.22010 · Zbl 0663.22010 · doi:10.1112/plms/s3-57.2.329
[7] L. MORRIS , Fundamental G-strata for Classical Groups (to appear, Duke Math. J.). Article | Zbl 0799.22009 · Zbl 0799.22009 · doi:10.1215/S0012-7094-91-06426-4
[8] A. MOY , Representations of U(2, 1) over a p-adic Field (Crelles J., Vol. 372, 1986 , pp. 178-208). Article | MR 88a:22031 | Zbl 0589.22015 · Zbl 0589.22015 · doi:10.1515/crll.1986.372.178
[9] A. MOY , Representations of GSp4 over a p-adic Field I (Comp. Math., Vol. 66, 1988 , pp. 237-284 ; II, ibid., Vol. 66, 1988 , pp. 285-328). Numdam | Zbl 0662.22012 · Zbl 0662.22012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.