Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
Compositio Mathematica, Volume 41 (1980) no. 2, pp. 245-285.
@article{CM_1980__41_2_245_0,
     author = {Bernstein, J. N. and Gelfand, S. I.},
     title = {Tensor products of finite and infinite dimensional representations of semisimple {Lie} algebras},
     journal = {Compositio Mathematica},
     pages = {245--285},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {41},
     number = {2},
     year = {1980},
     mrnumber = {581584},
     zbl = {0445.17006},
     language = {en},
     url = {http://www.numdam.org/item/CM_1980__41_2_245_0/}
}
TY  - JOUR
AU  - Bernstein, J. N.
AU  - Gelfand, S. I.
TI  - Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
JO  - Compositio Mathematica
PY  - 1980
SP  - 245
EP  - 285
VL  - 41
IS  - 2
PB  - Sijthoff et Noordhoff International Publishers
UR  - http://www.numdam.org/item/CM_1980__41_2_245_0/
LA  - en
ID  - CM_1980__41_2_245_0
ER  - 
%0 Journal Article
%A Bernstein, J. N.
%A Gelfand, S. I.
%T Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
%J Compositio Mathematica
%D 1980
%P 245-285
%V 41
%N 2
%I Sijthoff et Noordhoff International Publishers
%U http://www.numdam.org/item/CM_1980__41_2_245_0/
%G en
%F CM_1980__41_2_245_0
Bernstein, J. N.; Gelfand, S. I. Tensor products of finite and infinite dimensional representations of semisimple Lie algebras. Compositio Mathematica, Volume 41 (1980) no. 2, pp. 245-285. http://www.numdam.org/item/CM_1980__41_2_245_0/

[1] C. Zuckerman: Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. of Math. 106 (1977) 295-308. | MR | Zbl

[2] J.N. Bernstein, I.M. Gelfand and S.I. Gelfand: The structure of representations generated by vectors of highest weight, Funk. Anal. Appl. 51 (1971), N1, 1-9 (Russian). | MR | Zbl

[3] W. Borho and J.C. Jantzen: Uber primitive Ideale in der Einhullenden einer halbeinfachen Lie-Algebra. Inventiones Math. 39 (1977) 1-53. | MR | Zbl

[4] N.R. Wallach: On the Enright-Varadarajan modules, Ann. Sci. Ecole Norm. Sup. 9 (1976) 81-101. | Numdam | MR | Zbl

[5] A.W. Knapp and N.R. Wallach: Szegö kernels associated with discrete series, Inventiones Math. 34 (1976) 163-200. | MR | Zbl

[6] W. Schmidt: L2-cohomology and the discrete series, Ann. of Math. 103 (1976) 375-394. | MR | Zbl

[7] M.F. Atiyah and W. Schmidt: A geometric construction of the discrete series for semisimple Lie groups, Inventiones Math. 42 (1977) 1-62. | MR | Zbl

[8] B. Kostant: On tensor product of a finite and infinite dimensional representation. Jour. Func. Anal. v. 20 N 4 (1975) 257-285. | MR | Zbl

[9] M. Duflo: Sur la classification des ideaux primitifs dans l'algèbre envelloppante d'une algèbre de Lie semi-simple. Ann. of Math. 105 (1977) 107-120. | MR | Zbl

[10] D.P. Zhelobenko: Harmonic analysis on semisimple complex Lie groups, Moscow, "Nauka", 1974 (Russian). | MR

[11] M. Duflo: Représentations irréductibles des groupes semisimples complexes, Lecture Notes in Math. 497 (1975) 26-88. | MR | Zbl

[12] M. Duflo and N. Conze-Berline: Sur les représentations induites des groupes semi-simple complexes, Compositio Math. 34 (1977) 307-336. | Numdam | MR | Zbl

[13] H. Bass: Algebraic K-theory, Benjamin, 1968. | MR | Zbl

[14] B. Mitchell: Theory of categories, Academic Press, N.Y., 1965. | MR | Zbl

[15] S. Maclane: Categories for the Working Mathematician, Springer, New York-Berlin-Heidelberg, 1971. | MR | Zbl

[16] J. Dixmier: Algèbres envelloppantes. Paris, Gauthier-Villars, 1974. | MR | Zbl

[17] N. Bourbaki: Groupes et algèbres de Lie, Ch. 4, 5, 6. Paris, Hermann, 1968. | MR | Zbl

[18] B. Kostant: Lie group representations on polynomial rings, Amer. J. Math. 81 (1959) 937-1032. | MR

[19] J.N. Bernstein, I.M. Gelfand and S.I. Gelfand: On a category of G-modules. Funk. Anal. Appl. 10 (1976) N2, 1-8 (Russian). | MR | Zbl

[20] B. Kostant: A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959) 53-73. | MR | Zbl

[21] J. Lepowsky and N.R. Wallach: Finite- and infinite-dimensional representations of linear semisimple groups, Trans. Amer. Math. Soc. 184 (1973) 223-246. | MR | Zbl

[22] D. Vogan: Irreducible Characters of Semisimple Lie Groups I, Duke Math. J. 46 (1979) 61-00. | MR | Zbl

[23] J.C. Jantzen: Moduln mit einem höchsten Gewicht, Habilitationsschrift, Universität Bonn, 1977.

[24] T. Enright: On the Irreducibility of the Fundamental Series of a Real semisimple Lie Algebra, Ann. of Math. 110 (1979) 1-82. | MR | Zbl

[25] T. Enright: The Representations of Complex Semisimple Lie Groups (preprint).

[26] A. Joseph: Dixmier's Problem for Verma and Principal Series Submodules (preprint), December, 1978. | Zbl