@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://archive.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://archive.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://archive.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, Tome 41 (1980) no. 2, pp. 245-285. http://archive.numdam.org/item/CM_1980__41_2_245_0/
[1] Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. of Math. 106 (1977) 295-308. | MR | Zbl
:[2] The structure of representations generated by vectors of highest weight, Funk. Anal. Appl. 51 (1971), N1, 1-9 (Russian). | MR | Zbl
, and :[3] Uber primitive Ideale in der Einhullenden einer halbeinfachen Lie-Algebra. Inventiones Math. 39 (1977) 1-53. | MR | Zbl
and :[4] On the Enright-Varadarajan modules, Ann. Sci. Ecole Norm. Sup. 9 (1976) 81-101. | Numdam | MR | Zbl
:[5] Szegö kernels associated with discrete series, Inventiones Math. 34 (1976) 163-200. | MR | Zbl
and :[6] L2-cohomology and the discrete series, Ann. of Math. 103 (1976) 375-394. | MR | Zbl
:[7] A geometric construction of the discrete series for semisimple Lie groups, Inventiones Math. 42 (1977) 1-62. | MR | Zbl
and :[8] On tensor product of a finite and infinite dimensional representation. Jour. Func. Anal. v. 20 N 4 (1975) 257-285. | MR | Zbl
:[9] 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] Harmonic analysis on semisimple complex Lie groups, Moscow, "Nauka", 1974 (Russian). | MR
:[11] Représentations irréductibles des groupes semisimples complexes, Lecture Notes in Math. 497 (1975) 26-88. | MR | Zbl
:[12] Sur les représentations induites des groupes semi-simple complexes, Compositio Math. 34 (1977) 307-336. | Numdam | MR | Zbl
and :[13] Algebraic K-theory, Benjamin, 1968. | MR | Zbl
:[14] Theory of categories, Academic Press, N.Y., 1965. | MR | Zbl
:[15] Categories for the Working Mathematician, Springer, New York-Berlin-Heidelberg, 1971. | MR | Zbl
:[16] Algèbres envelloppantes. Paris, Gauthier-Villars, 1974. | MR | Zbl
:[17] Groupes et algèbres de Lie, Ch. 4, 5, 6. Paris, Hermann, 1968. | MR | Zbl
:[18] Lie group representations on polynomial rings, Amer. J. Math. 81 (1959) 937-1032. | MR
:[19] On a category of G-modules. Funk. Anal. Appl. 10 (1976) N2, 1-8 (Russian). | MR | Zbl
, and :[20] A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959) 53-73. | MR | Zbl
:[21] Finite- and infinite-dimensional representations of linear semisimple groups, Trans. Amer. Math. Soc. 184 (1973) 223-246. | MR | Zbl
and :[22] Irreducible Characters of Semisimple Lie Groups I, Duke Math. J. 46 (1979) 61-00. | MR | Zbl
:[23] Moduln mit einem höchsten Gewicht, Habilitationsschrift, Universität Bonn, 1977.
:[24] On the Irreducibility of the Fundamental Series of a Real semisimple Lie Algebra, Ann. of Math. 110 (1979) 1-82. | MR | Zbl
:[25] The Representations of Complex Semisimple Lie Groups (preprint).
:[26] Dixmier's Problem for Verma and Principal Series Submodules (preprint), December, 1978. | Zbl
: