A class of parabolic K-subgroups associated with symmetric K-varieties

A.G. Helminck, G.F. Helminck

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    Abstract

    Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, σ an involution of G defined over k, H a k-open subgroup of the fixed point group of σ, Gk (resp. Hk) the set of k-rational points of G (resp. H) and Gk/Hk the corresponding symmetric k-variety. A representation induced from a parabolic k-subgroup of G generically contributes to the Plancherel decomposition of L2(Gk/Hk) if and only if the parabolic k-subgroup is σ-split. So for a study of these induced representations a detailed description of the Hk-conjucagy classes of these σ-split parabolic k-subgroups is needed. In this paper we give a description of these conjugacy classes for general symmetric kvarieties. This description can be refined to give a more detailed description in a number of cases. These results are of importance for studying representations for real and p-adic symmetric k-varieties.
    Original languageEnglish
    Pages (from-to)4669-4691
    Number of pages23
    JournalTransactions of the American Mathematical Society
    Volume350
    Issue number11
    Publication statusPublished - 1998

    Keywords

    • METIS-140616
    • IR-97342

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