Meromorphic basis of \(H\)-invariant distribution vectors for generalized principal series of reductive symmetric spaces: Functional equation
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 \textit{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 \textit{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.
scientific article; zbMATH DE number 599798