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Vanishing of extensions of twisted Verma modules
Author(s):
Noriyuki
Abe
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3923-3926.
MSC (2000):
Primary 22E47;
Secondary 17B55
Posted:
June 12, 2009
MathSciNet review:
2529902
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Additional information
Abstract:
We prove a vanishing theorem of extension groups between twisted Verma modules.
References:
-
- [Abe]
- Noriyuki Abe, On the existence of homomorphisms between principal series of complex semisimple Lie groups, preprint.
- [AL03]
- H. H. Andersen and N. Lauritzen, Twisted Verma modules, Studies in memory of Issai Schur (Chevaleret/Rehovot, 2000), Progr. Math., vol. 210, Birkhäuser Boston, Boston, MA, 2003, pp. 1-26. MR 1985191 (2004d:17005)
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- J. N. Bernstein and S. I. Gelfand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), no. 2, 245-285. MR 581584 (82c:17003)
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- M. Delorme, Extensions in the Bernšteĭn-Gel fand-Gel fand category
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- Wilfried Schmid, Vanishing theorems for Lie algebra cohomology and the cohomology of discrete subgroups of semisimple Lie groups, Adv. in Math. 41 (1981), no. 1, 78-113. MR 625335 (82h:17009)
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Additional Information:
Noriyuki
Abe
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email:
abenori@ms.u-tokyo.ac.jp
DOI:
10.1090/S0002-9939-09-09958-4
PII:
S 0002-9939(09)09958-4
Keywords:
Category $\mathcal {O}$,
twisted Verma modules
Received by editor(s):
November 14, 2008,
Received by editor(s) in revised form:
March 2, 2009
Posted:
June 12, 2009
Communicated by:
Gail R. Letzter
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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