On the $\mathfrak n$-cohomology of limits of discrete series representations
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- by Wolfgang Soergel
- Represent. Theory 1 (1997), 69-82
- DOI: https://doi.org/10.1090/S1088-4165-97-00014-9
- Published electronically: March 7, 1997
Corrigendum: Represent. Theory 19 (2015), 1-2.
Abstract:
Using localization we translate the problem of computing the $\mathfrak {n}$-cohomology of limits of discrete series representations into a problem about the combinatorics of Weyl groups.References
- Alexandre Beĭlinson and Joseph Bernstein, Localisation de $g$-modules, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 15–18 (French, with English summary). MR 610137
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, Differential operators on the base affine space and a study of ${\mathfrak {g}}$-modules, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971) Halsted, New York, 1975, pp. 21–64. MR 0578996
- Alexander Beilinson, Victor Ginzburg, and Wolfgang Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), no. 2, 473–527. MR 1322847, DOI 10.1090/S0894-0347-96-00192-0
- 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.
- Jens Carsten Jantzen, Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 3, Springer-Verlag, Berlin, 1983 (German). MR 721170, DOI 10.1007/978-3-642-68955-0
- Ivan Mirković, On the localization for a singular infinitesimal character, Preprint, University of Massachusetts at Amherst, 1990.
- Dragan Miličić and Wolfgang Soergel, The composition series of modules induced from Whittaker modules, Preprint, 1995.
- Wilfried Schmid, $L^{2}$-cohomology and the discrete series, Ann. of Math. (2) 103 (1976), no. 2, 375–394. MR 396856, DOI 10.2307/1970944
- W. Soergel, $\mathfrak {n}$-cohomology of simple highest weight modules on walls and purity, Invent. Math. 98 (1989), no. 3, 565–580. MR 1022307, DOI 10.1007/BF01393837
- Floyd L. Williams, The $n$-cohomology of limits of discrete series, J. Funct. Anal. 80 (1988), no. 2, 451–461. MR 961909, DOI 10.1016/0022-1236(88)90011-0
Bibliographic Information
- Wolfgang Soergel
- Affiliation: Universität Freiburg Mathematisches Institut Eckerstraße 1 D-79104 Freiburg Germany
- Email: soergel@mathematik.uni-freiburg.de
- Received by editor(s): August 8, 1996
- Received by editor(s) in revised form: January 2, 1997
- Published electronically: March 7, 1997
- © Copyright 1997 By the author
- Journal: Represent. Theory 1 (1997), 69-82
- MSC (1991): Primary 22E46, 17B20
- DOI: https://doi.org/10.1090/S1088-4165-97-00014-9
- MathSciNet review: 1445512