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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 5, Issue 4


Volume 13 (2015)

The Cauchy Harish-Chandra Integral, for the pair $$\mathfrak{u}_{p,q} ,\mathfrak{u}_1 $$

Andrzej Daszkiewicz / Tomasz Przebinda
Published Online: 2007-12-01 | DOI: https://doi.org/10.2478/s11533-007-0023-3


For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.

Keywords: Orbital integrals; dual pairs

MSC: 22E45; 22E46

  • [1] A. Bouaziz: “Intégrales orbitales sur les algèbres de Lie réductives”, Invent. Math., Vol. 115, (1994), pp. 163–207. http://dx.doi.org/10.1007/BF01231757CrossrefGoogle Scholar

  • [2] A. Daszkiewicz and T. Przebinda: “The oscillator character formula, for isometry groups of split forms in deep stable range”, Invent. Math., Vol. 123, (1996), pp. 349–376. Google Scholar

  • [3] R. Howe: “Transcending classical invariant theory”, J. Amer. Math. Soc., Vol. 2, (1989), pp. 535–552. http://dx.doi.org/10.2307/1990942CrossrefGoogle Scholar

  • [4] L. Hörmander: The analysis of linear partial differential operators, I, Springer Verlag, Berlin, 1983. Google Scholar

  • [5] T. Przebinda: “A Cauchy Harish-Chandra integral, for a real reductive dual pair”, Invent. Math., Vol. 141, (2000), pp. 299–363. http://dx.doi.org/10.1007/s002220000070CrossrefGoogle Scholar

  • [6] W. Schmid: “On the characters of the discrete series. The Hermitian symmetric case”, Invent. Math., Vol. 30, (1975), pp. 47–144. http://dx.doi.org/10.1007/BF01389847CrossrefGoogle Scholar

  • [7] V.S. Varadarajan: Harmonic analysis on real reductive groups, Lecture Notes in Mathematics, Vol. 576, Springer Verlag, Berlin-New York, 1977. Google Scholar

  • [8] N. Wallach: Real Reductive Groups, I, Pure and Applied Mathematics, 132, Academic Press, Inc., Boston, MA, 1988. Google Scholar

About the article

Published Online: 2007-12-01

Published in Print: 2007-12-01

Citation Information: Open Mathematics, Volume 5, Issue 4, Pages 654–664, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-007-0023-3.

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© 2007 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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