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 Free Access

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.

**[ABV]**Jeffrey Adams, Dan Barbasch, and David A. Vogan Jr.,*The Langlands classification and irreducible characters for real reductive groups*, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992. MR**1162533****[B]**Dan Barbasch,*Unipotent representations for real reductive groups*, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 769–777. MR**1159263****[BV]**Dan Barbasch and David Vogan,*Weyl group representations and nilpotent orbits*, Representation theory of reductive groups (Park City, Utah, 1982) Progr. Math., vol. 40, Birkhäuser Boston, Boston, MA, 1983, pp. 21–33. MR**733804****[BB]**W. Borho and J.-L. Brylinski,*Differential operators on homogeneous spaces. III. Characteristic varieties of Harish-Chandra modules and of primitive ideals*, Invent. Math.**80**(1985), no. 1, 1–68. MR**784528**, 10.1007/BF01388547**[Ch]**Jen-Tseh Chang,*Remarks on localization and standard modules: the duality theorem on a generalized flag variety*, Proc. Amer. Math. Soc.**117**(1993), no. 3, 585–591. MR**1145942**, 10.1090/S0002-9939-1993-1145942-3**[Gi]**V. Ginsburg,*Characteristic varieties and vanishing cycles*, Invent. Math.**84**(1986), no. 2, 327–402. MR**833194**, 10.1007/BF01388811**[HMSW]**Henryk Hecht, Dragan Miličić, Wilfried Schmid, and Joseph A. Wolf,*Localization and standard modules for real semisimple Lie groups. I. The duality theorem*, Invent. Math.**90**(1987), no. 2, 297–332. MR**910203**, 10.1007/BF01388707**[Ka]**Masaki Kashiwara,*Systems of microdifferential equations*, Progress in Mathematics, vol. 34, Birkhäuser Boston, Inc., Boston, MA, 1983. Based on lecture notes by Teresa Monteiro Fernandes translated from the French; With an introduction by Jean-Luc Brylinski. MR**725502****[SV]**Wilfried Schmid and Kari Vilonen,*Characteristic cycles of constructible sheaves*, Invent. Math.**124**(1996), no. 1-3, 451–502. MR**1369425**, 10.1007/s002220050060**[SW]**Wilfried Schmid and Joseph A. Wolf,*A vanishing theorem for open orbits on complex flag manifolds*, Proc. Amer. Math. Soc.**92**(1984), no. 3, 461–464. MR**759674**, 10.1090/S0002-9939-1984-0759674-9**[Vo]**David A. Vogan Jr.,*Representations of real reductive Lie groups*, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 1981. MR**632407**

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

Email:
barbasch@math.cornell.edu

**Mladen Bozicevic**

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

Email:
bozicevi@cromath.math.hr

DOI:
https://doi.org/10.1090/S0002-9939-99-04482-2

Received by editor(s):
October 20, 1996

Received by editor(s) in revised form:
April 30, 1997

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1999
American Mathematical Society