Rayleigh triangles and non-matrix interpolation of matrix beta-integrals

Details Rayleigh triangles and non-matrix interpolation of matrix beta-integrals Rayleigh triangles and non-matrix interpolation of matrix beta-integrals

2003-01-08

arxiv.org/abs/math/0301070v1

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

We interpolate matrix beta-integrals of Siegel, Hua Loo Keng and Gindikin types with respect to dimension of the field. The domain of integration (Rayleigh triangles) imitates collections of all the eigenvalues of all the principal minors of a self-adjoint matrix. We also interpolate the Hua--Pickrell measures on inverse limits of symmetric spaces. Our family of integrals also contains the Selberg integral.

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