Tensor products of finite and infinite dimensional representations of semisimple Lie algebras

J. N. Bernstein; S. I. Gelfand

Compositio Mathematica (1980)

  • Volume: 41, Issue: 2, page 245-285
  • ISSN: 0010-437X

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Bernstein, J. N., and Gelfand, S. I.. "Tensor products of finite and infinite dimensional representations of semisimple Lie algebras." Compositio Mathematica 41.2 (1980): 245-285. <http://eudml.org/doc/89458>.

@article{Bernstein1980,
author = {Bernstein, J. N., Gelfand, S. I.},
journal = {Compositio Mathematica},
keywords = {infinite dimensional representations; semisimple Lie algebra; Verma modules; tensor product; projective functor; irreducible Harish-Chandra modules; principal series modules; category of finite modules; category O},
language = {eng},
number = {2},
pages = {245-285},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Tensor products of finite and infinite dimensional representations of semisimple Lie algebras},
url = {http://eudml.org/doc/89458},
volume = {41},
year = {1980},
}

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
PB - Sijthoff et Noordhoff International Publishers
VL - 41
IS - 2
SP - 245
EP - 285
LA - eng
KW - infinite dimensional representations; semisimple Lie algebra; Verma modules; tensor product; projective functor; irreducible Harish-Chandra modules; principal series modules; category of finite modules; category O
UR - http://eudml.org/doc/89458
ER -

References

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  1. [1] C. Zuckerman: Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. of Math.106 (1977) 295-308. Zbl0384.22004MR457636
  2. [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). Zbl0246.17008MR291204
  3. [3] W. Borho and J.C. Jantzen: Uber primitive Ideale in der Einhullenden einer halbeinfachen Lie-Algebra. Inventiones Math.39 (1977) 1-53. Zbl0327.17002MR453826
  4. [4] N.R. Wallach: On the Enright-Varadarajan modules, Ann. Sci. Ecole Norm. Sup.9 (1976) 81-101. Zbl0379.22008MR422518
  5. [5] A.W. Knapp and N.R. Wallach: Szegö kernels associated with discrete series, Inventiones Math.34 (1976) 163-200. Zbl0332.22015MR419686
  6. [6] W. Schmidt: L2-cohomology and the discrete series, Ann. of Math.103 (1976) 375-394. Zbl0333.22009MR396856
  7. [7] M.F. Atiyah and W. Schmidt: A geometric construction of the discrete series for semisimple Lie groups, Inventiones Math.42 (1977) 1-62. Zbl0373.22001MR463358
  8. [8] B. Kostant: On tensor product of a finite and infinite dimensional representation. Jour. Func. Anal. v. 20 N 4 (1975) 257-285. Zbl0355.17010MR414796
  9. [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. Zbl0346.17011MR430005
  10. [10] D.P. Zhelobenko: Harmonic analysis on semisimple complex Lie groups, Moscow, "Nauka", 1974 (Russian). Zbl0204.14403MR579170
  11. [11] M. Duflo: Représentations irréductibles des groupes semisimples complexes, Lecture Notes in Math.497 (1975) 26-88. Zbl0315.22008MR399353
  12. [12] M. Duflo and N. Conze-Berline: Sur les représentations induites des groupes semi-simple complexes, Compositio Math.34 (1977) 307-336. Zbl0389.22016MR439991
  13. [13] H. Bass: Algebraic K-theory, Benjamin, 1968. Zbl0174.30302MR249491
  14. [14] B. Mitchell: Theory of categories, Academic Press, N.Y., 1965. Zbl0136.00604MR202787
  15. [15] S. Maclane: Categories for the Working Mathematician, Springer, New York-Berlin-Heidelberg, 1971. Zbl0232.18001MR354798
  16. [16] J. Dixmier: Algèbres envelloppantes. Paris, Gauthier-Villars, 1974. Zbl0308.17007MR498737
  17. [17] N. Bourbaki: Groupes et algèbres de Lie, Ch. 4, 5, 6. Paris, Hermann, 1968. Zbl0483.22001MR240238
  18. [18] B. Kostant: Lie group representations on polynomial rings, Amer. J. Math.81 (1959) 937-1032. MR158024
  19. [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). Zbl0353.18013MR407097
  20. [20] B. Kostant: A formula for the multiplicity of a weight, Trans. Amer. Math. Soc.93 (1959) 53-73. Zbl0131.27201MR109192
  21. [21] J. Lepowsky and N.R. Wallach: Finite- and infinite-dimensional representations of linear semisimple groups, Trans. Amer. Math. Soc.184 (1973) 223-246. Zbl0279.17001MR327978
  22. [22] D. Vogan: Irreducible Characters of Semisimple Lie Groups I, Duke Math. J.46 (1979) 61-00. Zbl0398.22021MR523602
  23. [23] J.C. Jantzen: Moduln mit einem höchsten Gewicht, Habilitationsschrift, Universität Bonn, 1977. 
  24. [24] T. Enright: On the Irreducibility of the Fundamental Series of a Real semisimple Lie Algebra, Ann. of Math.110 (1979) 1-82. Zbl0417.17005MR541329
  25. [25] T. Enright: The Representations of Complex Semisimple Lie Groups (preprint). 
  26. [26] A. Joseph: Dixmier's Problem for Verma and Principal Series Submodules (preprint), December, 1978. Zbl0421.17005

Citations in EuDML Documents

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  1. Volodymyr Mazorchuk, Vanessa Miemietz, Serre functors for Lie algebras and superalgebras
  2. G. Van Dijk, M. Poel, The irreducible unitary GL ( n - 1 , ) -spherical representations of SL ( n , )
  3. William M. McGovern, A remark on differential operator algebras and an equivalence of categories
  4. Aboubeker Zahid, Les endomorphismes k -finis des modules de Whittaker
  5. O. Gabber, A. Joseph, Towards the Kazhdan-Lusztig conjecture
  6. O. Gabber, A. Joseph, On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula
  7. Ivan Penkov, Vera Serganova, On bounded generalized Harish-Chandra modules
  8. Patrick Polo, On the K -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case
  9. Hisayosi Matumoto, C - -Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets
  10. Hisayosi Matumoto, C - -Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations

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