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\(L^ p\)-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)

MSC:

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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