On the 𝔫-cohomology of limits of discrete series representations

Soergel, Wolfgang

doi:10.1090/S1088-4165-97-00014-9

On the $\mathfrak n$-cohomology of limits of discrete series representations
HTML articles powered by AMS MathViewer

by Wolfgang Soergel PDF

Represent. Theory 1 (1997), 69-82

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