Abstract

In this work we prove for all simple real groups of classical type, except for SO^*(n) and Sp(p,q), that if ν in a^* does not belong to C_ρ, the convex hull of the Weyl group orbit of ρ, then the signature of the Hermitian form attached to the irreducible subquotient of the principal spherical series corresponding to ν, with integral infinitesimal character, is indefinite on K-types in p.

Authors