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

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

2009-08-24

arxiv.org/abs/0908.3426v1

Trans. Amer. Math. Soc. (2011), electronic

Mathematics

Complex Variables

34 pages

Scientific paper

10.1090/S0002-9947-2011-05309-2

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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