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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

New identities of differential operators from orbital integrals on $\mathrm{GL}(r,\mathbf{C})$

Author(s): Paul Mezo
Journal: Proc. Amer. Math. Soc. 130 (2002), 3101-3110.
MSC (2000): Primary 22E30
Posted: March 14, 2002
MathSciNet review: 1908936
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Abstract | References | Similar articles | Additional information

Abstract: We derive identities of differential operators on complex general linear groups which appear in the differential equations satisfied by weighted orbital integrals. These identities stem from and have applications to comparisons of metaplectic coverings.

References:

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J. Arthur. Stabilization of a family of differential equations. Proc. Sympos. Pure Math. 68, Amer. Math. Soc., Providence, RI, 2000. MR 2001f:22025
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J. Arthur. The characters of discrete series as orbital integrals. Invent. Math., 32:205-261, 1976. MR 54:474

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J. Arthur. On a family of distributions obtained from Eisenstein series I: application of the Paley-Wiener theorem. Amer. J. Math., 104:1243-1288, 1982. MR 85k:22044

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J. Arthur. The local behaviour of weighted orbital integrals. Duke Math. J., 56:223-293, 1988. MR 89h:22036

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A. Knapp. Representation Theory of Semisimple Groups. Princeton University Press, Princeton, NJ, 1986. MR 87j:22022

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A. Knapp. Lie Groups Beyond an Introduction. Birkhäuser, 1996. MR 98b:22002

[Mez]
P. Mezo. Matching of weighted orbital integrals for metaplectic correspondences. Canad. Math. Bull. 44:482-490, 2001. CMP 2002:03

[Mez00]
P. Mezo. Some global correspondences for general linear groups and their metaplectic coverings. Technical report, Max-Planck-Institut für Mathematik Bonn, 2000. Preprint series number 55.

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Additional Information:

Paul Mezo
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: pmezo@math.toronto.edu

DOI: 10.1090/S0002-9939-02-06549-8
PII: S 0002-9939(02)06549-8
Received by editor(s): May 9, 2001
Posted: March 14, 2002
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 2002, American Mathematical Society




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