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Abstract: The paper is a survey of recent results in geometric representation theorydescribing group actions which induce multiplicity-free representations in thespaces of holomorphic functions. For connected compact Lie groups ofautomorphisms of Stein manifolds we characterize such actions in terms ofantiholomorphic involutions. Some proofs are given and some results are new.For example, spherical complex spaces are defined for arbitrary real forms ofcomplex reductive groups. Their properties, which we prove here, were knownonly for compact real forms. We also show that a complex compact homogeneousmanifold of a complex reductive group is spherical if and only if the fiber ofits Tits fibration is a complex torus.



Autor: Dmitri Akhiezer

Fuente: https://arxiv.org/







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