Abstract
LetG be a complex semisimple Lie group,B its Borel subgroup andX a flag variety ofG. We define a functor on the category ofB-equivariantD X-modules that corresponds, under the global section functor, to the Enright functor on the highest weight category. We use this to lift Enright functor to the mixed version of the highest weight category. As an application we obtain that the socle and the cosocle filtration of a primitive quotient of the enveloping algebra coincide.
Similar content being viewed by others
References
Beilinson, A., Bernstein, J.: A proof of Jantzen conjectures. Preprint
Bernstein, J., Gelfand, S.: Tensor products of finite and infinite dimensional representations of semisimple Lie algebras. Comp. Math.41, 245–285 (1980)
Borho, W., Brylinsky, J.-L.: Differential operators on homogeneous spaces III. Invent Math.80, 1–68 (1985)
Gabber, O., Joseph, A.: Towards the Kazhdan-Lusztig conjecture. Ann. Scien. Éc. Norm. Sup. (4)14, 261–302 (1981)
Jantzen, C.: Moduln mit einem höchsten gewicht (Lect. Notes Math., vol. 750) Berlin-Heidelberg-New York: Springer 1980
Joseph, A.: The Enright functor on the Bernstein-Gelfand-Gelfand categoryO. Invent. Math.67, 423–445 (1982)
Joseph, A.: Completion functors in theO category. In: Non-Commutative Harmonic Analysis and Lie Groups (Lect. Notes Math., vol. 1020, pp. 80–106) Berlin-Heidelberg-New York: Springer 1983
Joseph, A.: The primitive spectrum of an enveloping algebra. Astérisque173–174, 13–53 (1989)
Miliĉić, D.: Localization and representation theory of real reductive groups (forthcoming book)
Saito, M.: Modules de Hodge polarisables. Publ. RIMS, Kyoto Univ.24, 849–995 (1988)
Saito, M.: Mixed Hodge modules. Publ. RIMS, Kyoto Univ.26, 221–333 (1990)
Soergel, W.:n-Cohomology of simple highest weight modules on walls and purity. Invent. Math.98, 565–580 (1989)
Tanisaki, T.: Hodge modules, equivariantK-theory and Hecke algebras. Publ. RIMS, Kyoto Univ.23, 841–879 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Božiĉević, M. On the enright functor in the highest weight category. Manuscripta Math 85, 217–226 (1994). https://doi.org/10.1007/BF02568194
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02568194