Vecteurs distributionsH-invariants pour les s�ries principales g�n�ralis�es d'espaces symetriques reductifs et prolongement meromorphe d'int�grales d'Eisenstein

Smooth Fréchet globalizations of Harish-Chandra modules

“…fixed point sets of involutive automorphisms of g, are AC (Brylinski, Delorme, van den Ban; cf. [3], [2]). Here we only wish to discuss Casselman's result.…”

Spherical unitary highest weight representations

“…That this is nevertheless the case follows from [2] and [4] (see also [23] for the hyperfunction version). In the light of this result we only have to deal with the question of whether L(λ) is h-spherical.…”

“…For the unitary principal series induced from a parabolic subgroup we have for almost all parameters a complete description of (H −∞ ) H (cf. [1], [27] for the θτ -stable minimal parabolics and [4] for the general case). Discrete series on G/H were constructed in [12] (see also [30]) and in [3] it was shown that (H −∞ ) H is one-dimensional for all discrete series on G/H except for four types of exceptional symmetric spaces.…”

Algorithms for Twisted Involutions in Weyl Groups

“…They can be defined as the homogeneous spaces G/H, where G is a reductive Lie group and H is an open subgroup of the fixed point group of an involution of G. Initially mathematicians mainly studied the Riemannian symmetric spaces, i.e., the symmetric spaces for which H is a maximal compact subgroup of G. In the last 25 years the emphasis has shifted to include the general reductive symmetric spaces. Symmetric spaces are best known for their role in representation theory and many people have studied the representations associated with these real reductive symmetric spaces (see for example [HC84,FJ80,ŌS80,ŌM84,BD92,vdBS97,Del98]). …”