Vanishing of extensions of twisted Verma modules
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- by Noriyuki Abe PDF
- Proc. Amer. Math. Soc. 137 (2009), 3923-3926 Request permission
Abstract:
We prove a vanishing theorem of extension groups between twisted Verma modules.References
- Noriyuki Abe, On the existence of homomorphisms between principal series of complex semisimple Lie groups, preprint.
- 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
- J. N. Bernstein and S. I. Gel′fand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), no. 2, 245–285. MR 581584
- I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, A certain category of ${\mathfrak {g}}$-modules, Funkcional. Anal. i Priložen. 10 (1976), no. 2, 1–8 (Russian). MR 0407097
- Kevin J. Carlin, Extensions of Verma modules, Trans. Amer. Math. Soc. 294 (1986), no. 1, 29–43. MR 819933, DOI 10.1090/S0002-9947-1986-0819933-4
- M. Delorm, Extensions in the Bernšteĭn-Gel′fand-Gel′fand category ${\cal O}$. Applications, Funktsional. Anal. i Prilozhen. 14 (1980), no. 3, 77–78 (Russian). MR 583808
- James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. MR 1066460, DOI 10.1017/CBO9780511623646
- James E. Humphreys, Representations of semisimple Lie algebras in the BGG category $\scr {O}$, Graduate Studies in Mathematics, vol. 94, American Mathematical Society, Providence, RI, 2008. MR 2428237, DOI 10.1090/gsm/094
- Ronald Irving, Shuffled Verma modules and principal series modules over complex semisimple Lie algebras, J. London Math. Soc. (2) 48 (1993), no. 2, 263–277. MR 1231714, DOI 10.1112/jlms/s2-48.2.263
- 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, DOI 10.1016/S0001-8708(81)80005-9
Additional Information
- Noriyuki Abe
- Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
- MR Author ID: 858099
- Email: abenori@ms.u-tokyo.ac.jp
- Received by editor(s): November 14, 2008
- Received by editor(s) in revised form: March 2, 2009
- Published electronically: June 12, 2009
- Communicated by: Gail R. Letzter
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3923-3926
- MSC (2000): Primary 22E47; Secondary 17B55
- DOI: https://doi.org/10.1090/S0002-9939-09-09958-4
- MathSciNet review: 2529902