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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the cohomological dimension of the localization functor
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by Henryk Hecht and Dragan Miličić PDF
Proc. Amer. Math. Soc. 108 (1990), 249-254 Request permission

Abstract:

The left cohomological dimension of the localization functor is infinite for singular infinitesimal characters.
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 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 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 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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • 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