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Applications of Bruhat decompositions to complex hyperbolic geometry

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, American University, 20016, Washington, DC

    Jeffrey Hakim & Hanna Sandier

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  1. Jeffrey Hakim
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  2. Hanna Sandier
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Correspondence to Jeffrey Hakim.

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Hakim, J., Sandier, H. Applications of Bruhat decompositions to complex hyperbolic geometry. J Geom Anal 10, 435–453 (2000). https://doi.org/10.1007/BF02921944

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  • DOI: https://doi.org/10.1007/BF02921944

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