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Representation Theory
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On the ${{\frak n}} $-cohomology of limits of discrete series representations

Author(s): Wolfgang Soergel
Journal: Represent. Theory 1 (1997), 69-82.
MSC (1991): Primary 22E46, 17B20
Posted: March 7, 1997
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Abstract | References | Similar articles | Additional information

Abstract: Using localization we translate the problem of computing the ${{\frak n}} $-cohomology of limits of discrete series representations into a problem about the combinatorics of Weyl groups.


References:

[BB81]
Alexander A. Beilinson and Joseph N. Bernstein, Localisation de ${\frak    g}$-modules, C. R. Acad. Sci. Paris, Sér. 1 292 (1981), 15-18. MR 82k:14015

[BBD82]
Alexander A. Beilinson, Joseph N. Bernstein, and Pierre Deligne, Faisceaux pervers, Astérisque 100 (1982), 1-172. MR 86g:32015

[BGG75]
Joseph N. Bernstein, Israel M. Gelfand, and Sergei I. Gelfand, Differential operators on the base affine space and a study of ${\frak    g}$-modules, Lie groups and their Representations (I. M. Gelfand, ed.), Halsted: New York, 1975, pp. 21-64. MR 58:28285

[BGS96]
Alexander A. Beilinson, Victor Ginzburg, and Wolfgang Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), no. 2, 473-527. MR 96k:17010

[Car96]
Henri Carayol, Limites dégénérées de séries discrètes, formes automorphes et variétés de Griffiths-Schmid: Le cas du groupe $U(2,1)$, Prépublication IRMA 1996/10 (Strasbourg), 1996.

[Jan83]
Jens C. Jantzen, Einhüllende Algebren halbeinfacher Lie-Algebren, Springer, 1983. MR 86c:17011

[Mir90]
Ivan Mirkovi\'{c}, On the localization for a singular infinitesimal character, Preprint, University of Massachusetts at Amherst, 1990.

[MS95]
Dragan Mili\v{c}i\'{c} and Wolfgang Soergel, The composition series of modules induced from Whittaker modules, Preprint, 1995.

[Sch76]
Wilfried Schmid, ${L^2}$-cohomology and the discrete series, Annals of Mathematics 103 (1976), 375-394. MR 53:716

[Soe89]
Wolfgang Soergel, ${{\frak n}} $-cohomology of simple highest weight modules on walls and purity, Inventiones 98 (1989), 565-580. MR 90M:22037

[Wil88]
Floyd L. Williams, The ${{\frak n}} $-cohomology of limits of discrete series, Journal of functional analysis 80 (1988), 451-461. MR 89j:22036


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Additional Information:

Wolfgang Soergel
Affiliation: Universität Freiburg Mathematisches Institut Eckerstraße 1 D-79104 Freiburg Germany
Email: soergel@mathematik.uni-freiburg.de

DOI: 10.1090/S1088-4165-97-00014-9
PII: S 1088-4165(97)00014-9
Received by editor(s): August 8, 1996
Received by editor(s) in revised form: January 2, 1997
Posted: March 7, 1997
Copyright of article: Copyright 1997, By the author


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