\(L^ p\)-analysis on homogeneous manifolds of reductive type and representation theory. (English) Zbl 0883.22015

\(L^p\)-analysis on homogeneous manifolds of reductive type and representation theory are discussed. The main results are: Let \(G\) be a real reductive linear Lie group, \(K\) a maximal compact subgroup of \(G\), and \(\theta\) the corresponding Cartan involution, \(H\) a closed \(\theta\)-stable subgroup of \(G\) with finitely many connected components. There are four sections in this paper: (1) Invariant measures on homogeneous manifolds of reductive type. (2) Irreducible representations in \(L^p(G/H)\). (3) Holomorphic discrete series representations. (4) Some valuable examples are given.
Reviewer: Su Weiyi (Nanjing)


22E46 Semisimple Lie groups and their representations
43A85 Harmonic analysis on homogeneous spaces
22E15 General properties and structure of real Lie groups
22E30 Analysis on real and complex Lie groups
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