Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The associated variety
of an induced representation

Authors: Dan Barbasch and Mladen Bozicevic
Journal: Proc. Amer. Math. Soc. 127 (1999), 279-288
MSC (1991): Primary 22E46
MathSciNet review: 1458862
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E46

Retrieve articles in all journals with MSC (1991): 22E46

Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

Mladen Bozicevic
Affiliation: University of Zagreb, Geotechnical Faculty, 42000 Varaždin, Croatia

Received by editor(s): October 20, 1996
Received by editor(s) in revised form: April 30, 1997
Communicated by: Roe Goodman
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society