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

The associated variety of an induced representation

Author(s): Dan Barbasch; Mladen Bozicevic
Journal: Proc. Amer. Math. Soc. 127 (1999), 279-288.
MSC (1991): Primary 22E46
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Abstract | References | Similar articles | Additional information

Abstract: This paper studies the behavior of the associated variety under induction from real parabolic subgroups. We derive a formula for the associated variety of an induced module which is analogous to the formula for the wave front set of a derived functor module obtained by Barbasch and Vogan.


References:

[ABV]
J. Adams, D. Barbasch, D. Vogan, The Langlands classification and irreducible representations for real reductive groups, Birkhäuser. MR 93j:22001

[B]
D. Barbasch, Unipotent representations for real reductive groups, Proceedings of ICM 1990, Springer Verlag, 1991, pp. 769-777. MR 93m:22012

[BV]
D. Barbasch and D. Vogan, Weyl Group Representations and Nilpotent Orbits, Representation Theory of Reductive Groups (P.C. Trombi, eds.), Birkhäuser-Boston, 1983, pp. 21-32. MR 85g:22025

[BB]
W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces III, Invent. Math. 80 (1985), 1-68. MR 87i:22045

[Ch]
J.-T. Chang, Remarks on localization and standard modules: the duality theorem on a generalized flag variety, Proc. of the Amer. Math. Soc. 117 (1993), 585-591. MR 93d:22016

[Gi]
V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327-402. MR 87j:32030

[HMSW]
H. Hecht, D. Mili\v{c}i\'{c}, W. Schmid, J. Wolf, Localization and standard modules for real semisimple groups I: The duality theorem, Invent. Math. 90 (1987), 297-332. MR 89e:22025

[Ka]
M. Kashiwara, Systems of microdifferential equations, Progress in Math. 34, Birkhäuser, 1983. MR 86b:58113

[SV]
W. Schmid and K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1996), 451-502. MR 96k:32016

[SW]
W. Schmid and J. Wolf, A vanishing theorem for open orbits on complex flag manifolds, Proc. of the Amer. Math. Soc. 92 (1984), 461-464. MR 85i:32029

[Vo]
D.Vogan, Representations of real reductive Lie groups, Progress in Math. 15, Birkhäuser, 1981. MR 83c:22022


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Additional Information:

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: barbasch@math.cornell.edu

Mladen Bozicevic
Affiliation: University of Zagreb, Geotechnical Faculty, 42000 Varazdin, Croatia
Email: bozicevi@cromath.math.hr

DOI: 10.1090/S0002-9939-99-04482-2
PII: S 0002-9939(99)04482-2
Received by editor(s): October 20, 1996
Received by editor(s) in revised form: April 30, 1997
Communicated by: Roe Goodman
Copyright of article: Copyright 1999, American Mathematical Society


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