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

• Autorzy: Andrzej Daszkiewicz , Tomasz Przebinda
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Orbital integrals; dual pairs

Kategorie tematyczne

• 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods
• 22E46: Semisimple Lie groups and their representations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 654-664

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

Andrzej Daszkiewicz

• N. Copernicus University

autor

Tomasz Przebinda

• University of Oklahoma

Bibliografia

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• [4] L. Hörmander: The analysis of linear partial differential operators, I, Springer Verlag, Berlin, 1983.
• [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/s002220000070
• [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/BF01389847
• [7] V.S. Varadarajan: Harmonic analysis on real reductive groups, Lecture Notes in Mathematics, Vol. 576, Springer Verlag, Berlin-New York, 1977.
• [8] N. Wallach: Real Reductive Groups, I, Pure and Applied Mathematics, 132, Academic Press, Inc., Boston, MA, 1988.

Identyfikatory

DOI

10.2478/s11533-007-0023-3