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)

 
 

 

$\mathfrak{n}$-homology of generic
representations for $GL(N)$


Authors: Jen-Tseh Chang and James W. Cogdell
Journal: Proc. Amer. Math. Soc. 127 (1999), 1251-1256
MSC (1991): Primary 22E46
DOI: https://doi.org/10.1090/S0002-9939-99-04623-7
MathSciNet review: 1473658
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We compute the $\mathfrak{n}$-homology for a class of representations of
$GL(N,\mathbb{R})$ and $GL(N,\mathbb{C})$ which admit a Whittaker model. They are all completely reducible.


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

  • [1] W. Casselman, Jacquet modules for real reductive groups, Proceedings of the International Congress of Mathematicians, Helsinki, 1978, 557-563. MR 83h:22025
  • [2] J.-T. Chang, Special $K$-types, tempered characters and the Beilinson-Bernstein realization, Duke Math. J. 56 (1988), 345-383. MR 89k:22028
  • [3] J. Cogdell and I.I. Piatetski-Shapiro, Derivatives and L-functions for $GL_{n}$, to appear in a volume dedicated to B. Moishezon.
  • [4] H. Hecht and W. Schmid, Characters, asymptotics and $\mathfrak{n}$-homology of Harish-Chandra modules, Acta Math. 151 (1983), 49-151. MR 84k:22026
  • [5] D. Vogan Jr, Gelfand-Kirillov dimensions for Harish-Chandra modules, Inv. math. 48 (1978), 75-98. MR 58:22205
  • [6] D. Vogan Jr., Representations of Real Reductive Lie Groups, Birkäuser, Boston, 1981. MR 83c:22022
  • [7] N. Wallach, Real Reductive Groups II, Academic Press, San Diego, 1992. MR 93m:22018

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

Jen-Tseh Chang
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613
Email: changj@math.okstate.edu

James W. Cogdell
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613
Email: cogdell@math.okstate.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04623-7
Received by editor(s): April 30, 1996
Received by editor(s) in revised form: August 20, 1997
Additional Notes: The second author was partially supported by a grant from the NSA
Communicated by: Roe Gooodman
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society