K-invariant cusp forms for reductive symmetric spaces of split rank one

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Let G/H be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for G/H. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of G/H.
Original languageEnglish
JournalForum Mathematicum
Issue number2
Pages (from-to)341-349
Number of pages8
Publication statusPublished - 2019

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