×

zbMATH — the first resource for mathematics

Conical vectors in induced modules. (English) Zbl 0311.17002

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
16Gxx Representation theory of associative rings and algebras
17B20 Simple, semisimple, reductive (super)algebras
17B35 Universal enveloping (super)algebras
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] I. N. Bernšteĭn, I. M. Gel\(^{\prime}\)fand, and S. I. Gel\(^{\prime}\)fand, Differential operators on the fundamental affine space, Dokl. Akad. Nauk SSSR 195 (1970), 1255 – 1258 (Russian).
[2] Универсал\(^{\приме}\)ные обертывающие алгебры., Издат. ”Мир”, Мосцощ, 1978 (Руссиан). Транслатед фром тхе Френч бы Ју. А. Бахтурин; Едитед бы Д. П. Žелобенко.
[3] Michel Duflo, Représentations irréductibles des groupes semi-simples complexes, Analyse harmonique sur les groupes de Lie (Sém., Nancy-Strasbourg, 1973 – 75), Springer, Berlin, 1975, pp. 26 – 88. Lecture Notes in Math., Vol. 497 (French). · Zbl 0315.22008
[4] Harish-Chandra, Representations of semisimple Lie groups. II, Trans. Amer. Math. Soc. 76 (1954), 26 – 65. · Zbl 0055.34002
[5] SigurÄ’ur Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math. 5 (1970), 1 – 154 (1970). · Zbl 0209.25403 · doi:10.1016/0001-8708(70)90037-X · doi.org
[6] Bertram Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627 – 642. · Zbl 0229.22026
[7] J. Lepowsky, Algebraic results on representations of semisimple Lie groups, Trans. Amer. Math. Soc. 176 (1973), 1 – 44. · Zbl 0264.22012
[8] G. D. Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973. Annals of Mathematics Studies, No. 78. · Zbl 0265.53039
[9] C. Rader, Spherical functions on semisimple Lie groups, Thesis and unpublished supplements, University of Washington, 1971.
[10] Daya-Nand Verma, Structure of certain induced representations of complex semisimple Lie algebras, Bull. Amer. Math. Soc. 74 (1968), 160 – 166. · Zbl 0157.07604
[11] Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 19. · Zbl 0265.22022
[12] M. Hu, Determination of the conical distributions for rank one symmetric spaces, Thesis, Massachusetts Institute of Technology, 1973.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.