1,098 research outputs found
On the realization of Riemannian symmetric spaces in Lie groups
In this paper we give a realization of some symmetric space G/K as a closed
submanifold P of G. We also give several equivalent representations of the
submanifold P. Some properties of the set gK\cap P are also discussed, where gK
is a coset space in G.Comment: 8 page
On the realization of Riemannian symmetric spaces in Lie groups II
In this paper we generalize a result in [1], showing that an arbitrary
Riemannian symmetric space can be realized as a closed submanifold of a
covering group of the Lie group defining the symmetric space. Some properties
of the subgroups of fixed points of involutions are also proved.Comment: 6 page
Holomorphic harmonic analysis on complex reductive groups
We define the holomorphic Fourier transform of holomorphic functions on
complex reductive groups, prove some properties like the Fourier inversion
formula, and give some applications. The definition of the holomorphic Fourier
transform makes use of the notion of -admissible measures. We prove that
-admissible measures are abundant, and the definition of holomorphic Fourier
transform is independent of the choice of -admissible measures.Comment: 15 pages, revision of a preprint by the first author in 200
A Generalization of Random Matrix Ensemble I: General Theory
We give a generalization of the random matrix ensembles, including all
lassical ensembles. Then we derive the joint density function of the
generalized ensemble by one simple formula, which give a direct and unified way
to compute the density functions for all classical ensembles and various kinds
of new ensembles. An integration formula associated with the generalized
ensemble is also given. We also give a classification scheme of the generalized
ensembles, which will include all classical ensembles and some new ensembles
which were not considered before.Comment: 15 page
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