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Meromorphic basis of $$H$$-invariant distribution vectors for generalized principal series of reductive symmetric spaces: Functional equation. (Base méromorphe de vecteurs distributions $$H$$-invariants pour les séries principales généralisées d’espaces symétriques réductifs: Equation fonctionnelle.) (French) Zbl 0831.22004
Let $$G$$ be a reductive group of Harish-Chandra class, $$\sigma$$ an involution of $$G$$, $$\vartheta$$ a Cartan involution of $$G$$ commuting with $$\sigma$$, $$H$$ an open subgroup of the group of fixed points for $$\sigma$$. The authors generalize certain results by E. van den Ban [Ann. Sci. Ec. Norm. Super., IV. Ser. 21, 359-412 (1988; Zbl 0714.22009)] and [J. Funct. Anal. 109, 331-441 (1992; Zbl 0791.22008)] concerning spaces of $$H$$-invariant distribution vectors of induced representations from a minimal $$\sigma \vartheta$$-stable parabolic subgroup $$P$$ of $$G$$ to the not necessarily minimal case. The method employs the approach of F. Bruhat [Bull. Soc. Math. France 84, 97-205 (1956; Zbl 0074.103)]. As a result, a certain meromorphic basis for the mentioned space is found. – The paper is intended for specialists, it involves numerous references to recent works. A large number of advanced results cannot be adequately reviewed here for technical reasons.
Reviewer: J.Chrastina (Brno)

##### MSC:
 2.2e+47 Semisimple Lie groups and their representations
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