$R$--groups and elliptic representations for similitude groups

Details $R$--groups and elliptic representations for similitude groups $R$--groups and elliptic representations for similitude groups

1994-12-20

arxiv.org/abs/math/9412206v1

Mathematics

Representation Theory

28 pages

Scientific paper

The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over $p$\snug-adic groups of characteristic zero is studied. The components of representations induced from discrete series of proper parabolic subgroups are classified in terms of $R$\snug-groups. Multiplicity one is proved. The tempered elliptic spectrum is identified, and the relation between elliptic characters appearing in a given induced representation is determined. Those irreducible tempered representations which are not elliptic and not fully induced from elliptic tempered representations are described.

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