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The restriction of \(A_ q(\lambda)\) to reductive subgroups. (English) Zbl 0826.22014
Sei \(G\) eine reelle reduktive lineare Liegruppe und \(G'\) eine reduktive Untergruppe. Eine unitäre Darstellung \(\pi\) heißt \(G'\)-zulässig, falls die Einschränkung \(\pi|_{G'}\) in eine direkte Summe irreduzibler Darstellungen von \(G'\) mit endlicher Multiplizität aufspaltet. Falls \(G'\) eine maximale kompakte Untergruppe ist, gilt dies (Harish-Chandra) und für \(\pi = A_q (\lambda)\) ist eine explizite Zerlegungsformel bekannt (verallg. Blattner-Formel).
In der vorliegenden Arbeit kündigt der Verfasser ein solches Zulässigkeitsresultat für reduktive symmetrische Paare an. Weiter betrachtet er Restriktionen von Darstellungen (diskrete Serie) in Verbindung mit homogenen Räumen. Damit ergeben sich Existenzaussagen für diskrete Serien gewisser nicht-symmetrischer sphärischer homogener Räume. Schließlich werden noch explizite Verzweigungsformeln angegeben.

MSC:
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
22E15 General properties and structure of real Lie groups
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