不变锥与复Olshanskii半群的边界轨层和面
Boundary orbit strata and faces of invariant cones and complex Olshanskii semigroups
摘要：
设D=G/K是不可约Hermitian对称整环。则G包含在一个复化中，并且存在复化的一个闭复子半群，即所谓的极小Olshanskii半群，其特征在于G的所有全纯离散级数表示全纯地延伸到它。本文将极小Olshanskii半群的K-轨道型层作为K-等变纤维丛给出了详细而完整的描述。它们是由G的李代数的极小不变锥面的共轭类给出的。
英文摘要：
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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