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On the cohomological dimension of the localization functor


Authors: Henryk Hecht and Dragan Miličić
Journal: Proc. Amer. Math. Soc. 108 (1990), 249-254
MSC: Primary 17B35
DOI: https://doi.org/10.1090/S0002-9939-1990-0984793-4
MathSciNet review: 984793
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Abstract: The left cohomological dimension of the localization functor is infinite for singular infinitesimal characters.


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  • 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 generalization of Casselman’s submodule theorem, in "Representation theory of reductive groups," Birkhäuser, Boston, 1983, pp. 35-52. N. Bourbaki, Algèbre commutative, Masson, Paris. ---, Groupes et algebres de Lie, Masson, Paris. A Grothendieck, Eléments de géométrie algébrique IV, Publ. I.H.E.S. No. 20 (1964).
  • Henryk Hecht, Dragan Miličić, Wilfried Schmid, and Joseph A. Wolf, Localization and standard modules for real semisimple Lie groups. I. The duality theorem, Invent. Math. 90 (1987), no. 2, 297–332. MR 910203, DOI https://doi.org/10.1007/BF01388707
  • A. Joseph and J. T. Stafford, Modules of ${\mathfrak k}$-finite vectors over semisimple Lie algebras, Proc. London Math. Soc. (3) 49 (1984), no. 2, 361–384. MR 748996, DOI https://doi.org/10.1112/plms/s3-49.2.361
  • D. Miličić, Localization and representation theory of reductive Lie groups," (mimeographed notes, to appear).

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