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Invariant analytic domains in complex semisimple groups

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Abstract

LetH ℝ be a real form of a complex semisimple group. We study certain naturally-defined analytic domains in the complexified groupH C which are invariant under left and right translation byH ℝ. In particular, we give a detailed description of these sets in terms of cross-sections inside maximal R-tori ofH. It has been suggested by I. M. Gelfand and S. G. Gindikin that complex analytic objects related to these domains will provide explicit realizations of unitary representations ofH ℝ.

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Authors and Affiliations

  1. Department of Mathematics, Ball State University, 47306-0490, Muncie, IN, USA

    R. J. Bremigan

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  1. R. J. Bremigan
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Research partially supported by NSA grant MDA904-96-1-0050.

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Bremigan, R.J. Invariant analytic domains in complex semisimple groups. Transformation Groups 1, 279–305 (1996). https://doi.org/10.1007/BF02549210

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  • DOI: https://doi.org/10.1007/BF02549210

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