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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:
22E46 Semisimple Lie groups and their representations
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