Indecomposable representations of semisimple Lie groups
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- by Birgit Speh PDF
- Trans. Amer. Math. Soc. 265 (1981), 1-34 Request permission
Abstract:
Let $G$ be a semisimple connected linear Lie group, ${\pi _1}$ a finite-dimensional irreducible representation of $G$, ${\pi _2}$ an infinite-dimensional irreducible representation of $G$ which has a nontrivial extension with ${\pi _1}$. We study the category of all Harish-Chandra modules whose composition factors are equivalent to ${\pi _1}$ and ${\pi _2}$References
-
A. Borel and N. Wallach, Seminar on the cohomology of discrete subgroups of semisimple groups, Institute for Advanced Study, Princeton, N. J., 1976-1977.
W. Casselman, The differential equations satisfied by matrix coefficients, manuscript, 1975.
- Vlastimil Dlab and Claus Michael Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 6 (1976), no. 173, v+57. MR 447344, DOI 10.1090/memo/0173
- I. M. Gel′fand, The cohomology of infinite dimensional Lie algebras: some questions of integral geometry, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 95–111. MR 0440631 I. M. Gelfand, M. I. Graev and V. A. Ponomarev, The classification of the linear representations of the group ${\text {SL(2,}}{\mathbf {C}})$, Soviet Math. Dokl. 11 (1970), 1319-1323.
- I. M. Gel′fand and V. A. Ponomarev, The category of Harish-Chandra modules over the Lie algebra of the Lorentz group, Dokl. Akad. Nauk SSSR 176 (1967), 243–246 (Russian). MR 0223504 —, Classification of indecomposable infinitesimal representations of the Lorentz group, Soviet. Math. Dokl. 8 (1967), 1114-1117.
- Harish-Chandra, Representations of semisimple Lie groups. II, Trans. Amer. Math. Soc. 76 (1954), 26–65. MR 58604, DOI 10.1090/S0002-9947-1954-0058604-0
- A. W. Knapp and E. M. Stein, Singular integrals and the principal series. IV, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2459–2461. MR 376964, DOI 10.1073/pnas.72.6.2459 R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Institute for Advanced Study, Princeton, N. J., mimeographed notes, 1973.
- Dragan Miličić, Asymptotic behaviour of matrix coefficients of the discrete series, Duke Math. J. 44 (1977), no. 1, 59–88. MR 430164 —, Jacquet modules for real groups and Langlands classification of representations, Lecture in Oberwolfach, June 1977.
- V. Dlab (ed.), Representations of algebras, Lecture Notes in Mathematics, Vol. 488, Springer-Verlag, Berlin-New York, 1975. MR 0382322 G. Schiffman, Integrales d’enterlacement et fonctions de Whittaker, Bull. Soc. Math. France 99 (1971), 3-72.
- Birgit Speh and David A. Vogan Jr., Reducibility of generalized principal series representations, Acta Math. 145 (1980), no. 3-4, 227–299. MR 590291, DOI 10.1007/BF02414191
- David A. Vogan Jr., Irreducible characters of semisimple Lie groups. I, Duke Math. J. 46 (1979), no. 1, 61–108. MR 523602 —, Lie algebra cohomology and the representations of semisimple Lie groups, Thesis, M.I.T., Cambridge, Mass., 1976.
- Gregg Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. of Math. (2) 106 (1977), no. 2, 295–308. MR 457636, DOI 10.2307/1971097
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 265 (1981), 1-34
- MSC: Primary 22E45; Secondary 20G05
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607104-1
- MathSciNet review: 607104