$\mathfrak n$-homology of generic representations for $GL(N)$
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- by Jen-Tseh Chang and James W. Cogdell PDF
- Proc. Amer. Math. Soc. 127 (1999), 1251-1256 Request permission
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
- W. Casselman, Jacquet modules for real reductive groups, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 557–563. MR 562655
- Jen-Tseh Chang, Special $K$-types, tempered characters and the Beilinson-Bernstein realization, Duke Math. J. 56 (1988), no. 2, 345–383. MR 932850, DOI 10.1215/S0012-7094-88-05614-1
- J. Cogdell and I.I. Piatetski-Shapiro, Derivatives and L-functions for $GL_{n}$, to appear in a volume dedicated to B. Moishezon.
- Henryk Hecht and Wilfried Schmid, Characters, asymptotics and ${\mathfrak {n}}$-homology of Harish-Chandra modules, Acta Math. 151 (1983), no. 1-2, 49–151. MR 716371, DOI 10.1007/BF02393204
- David A. Vogan Jr., Gel′fand-Kirillov dimension for Harish-Chandra modules, Invent. Math. 48 (1978), no. 1, 75–98. MR 506503, DOI 10.1007/BF01390063
- David A. Vogan Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 1981. MR 632407
- Nolan R. Wallach, Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1992. MR 1170566
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
- MR Author ID: 50230
- Email: cogdell@math.okstate.edu
- 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
- © Copyright 1999 American Mathematical Society
- 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