Applications of Bruhat decompositions to complex hyperbolic geometry |
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Authors: | Jeffrey Hakim Hanna Sandier |
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Institution: | (1) Department of Mathematics and Statistics, American University, 20016 Washington, DC |
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Abstract: | The double coset space AΛ (n, ℂ) / U (n − 1, 1) is studied, where A consists of the diagonal matrices in GL (n, ℂ). This space
naturally arises in the harmonic analysis on the hermitian symmetric space GL (n, ℂ) / U (n − 1, 1). It is shown here that
these double cosets also represent a class of basic invariants related to complex hyperbolic geometry. An algebraic parametrization
for the double cosets is given and it is shown how this may be used to conveniently compute the geometric invariants. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 51M10 15A23 |
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