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arXiv · 0908.3426

Boundary orbit strata and faces of invariant cones and complex Olshanskii semigroups

Alexander Alldridge
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Abstract

Let D=G/K be an irreducible Hermitian symmetric domain. Then G is contained in a complexification, and there exists a closed complex subsemigroup, the so-called minimal Olshanskii semigroup, of the complexification characterised by the fact that all holomorphic discrete series representations of G extend holomorphically to it. Parallel to the classical theory of boundary strata for the symmetric domain D, due to Koranyi and Wolf, we give a detailed and complete description of the K-orbit type strata of the minimal Olshanskii semigroup, as K-equivariant fibre bundles. They are given by the conjugacy classes of faces of the minimal invariant cone in the Lie algebra of G.

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Alexander Alldridge. 2009-08-24. Boundary orbit strata and faces of invariant cones and complex Olshanskii semigroups. https://doi.org/10.1090/s0002-9947-2011-05309-2

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