\(R\)-groups and elliptic representations for similitude groups (Q1359504)

The tempered spectrum of the similitude groups of nondegenerate symplectic, hermitian, or split orthogonal forms defined over \(p\)-adic groups of characteristic zero is studied. The components of representations induced from discrete series of proper parabolic subgroups are classified in terms of \(R\)-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.