×

zbMATH — the first resource for mathematics

On the annihilators of the simple subquotients of the principal series. (English) Zbl 0386.17004

MSC:
17B35 Universal enveloping (super)algebras
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] W. BORHO , Recent Advances in the Enveloping Algebras of Semisimple Lie Algebras (Séminaire Bourbaki, No. 489, November 1976 ). Numdam | Zbl 0394.17005 · Zbl 0394.17005 · numdam:SB_1976-1977__19__1_0 · eudml:109903
[2] W. BORHO und H. KRAFT , Über die Gelfand-Kirillov-Dimension (Math. Ann., Vol. 220, 1976 , pp. 1-24). MR 54 #367 | Zbl 0306.17005 · Zbl 0306.17005 · doi:10.1007/BF01354525 · eudml:162801
[3] W. BORHO und J. C. JANTZEN , Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra (Invent. Math., Vol. 39, 1977 , pp. 1-53). MR 56 #12079 | Zbl 0327.17002 · Zbl 0327.17002 · doi:10.1007/BF01695950 · eudml:142455
[4] W. BORHO und J. C. JANTZEN (to appear).
[5] N. CONZE-BERLINE et M. DUFLO , Sur les représentations des groupes semi-simple complexes , Compos. Math., Vol. 34, 1977 , pp. 307-336). Numdam | MR 55 #12872 | Zbl 0389.22016 · Zbl 0389.22016 · numdam:CM_1977__34_3_307_0 · eudml:89330
[6] M. DUFLO , Représentations irréductibles des groupes semi-simple complexes (Lecture Notes, No. 497, 1975 , pp. 26-88). MR 53 #3198 | Zbl 0315.22008 · Zbl 0315.22008
[7] M. DUFLO , Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple (Ann. Math., Vol. 105, 1977 , pp. 107-120). MR 55 #3013 | Zbl 0346.17011 · Zbl 0346.17011 · doi:10.2307/1971027 · www.jstor.org
[8] J. DIXMIER , Algèbres enveloppantes (Cahiers scientifiques, Vol. XXXVII, Gauthier-Villars, Paris, 1974 ). MR 58 #16803a | Zbl 0308.17007 · Zbl 0308.17007
[9] J. C. JANTZEN , Kontravariante formen auf induzierte Darstellungen halbeinfacher Lie-Algebren (Math. Ann., Vol. 226, 1977 , pp. 53-65). MR 55 #12783 | Zbl 0372.17003 · Zbl 0372.17003 · doi:10.1007/BF01391218 · eudml:162940
[10] A. JOSEPH , A Characteristic Variety for the Primitive Spectrum of a Semisimple Lie Algebra , preprint, Bonn, 1976 . Short version in Lecture Notes, No. 587. 1977 , pp. 102-118. MR 56 #8645 | Zbl 0374.17004 · Zbl 0374.17004
[11] N. N. SHAPOVALOV , On a Bilinear Form on the Universal Enveloping Algebra of a Complex Semisimple Lie Algebra (Funkt. Analiz i Ego Pril., Vol. 6, 1972 , pp. 65-70). MR 47 #8644 | Zbl 0283.17001 · Zbl 0283.17001 · doi:10.1007/BF01077650
[12] N. SPALTENSTEIN , Remarques sur certaines relations d’équivalence dans les groupes de Weyl , preprint Warwick, 1977 .
[13] N. CONZE et J. DIXMIER , Idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semisimple (Bull. Sc. math., 2e série, Vol. 96, 1972 , pp. 339-351). MR 48 #356 | Zbl 0246.17009 · Zbl 0246.17009
[14] J. C. JANTZEN (to appear).
[15] A. JOSEPH , Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules [J. Lond. Math. Soc. (to appear)]. Zbl 0401.17007 · Zbl 0401.17007 · doi:10.1112/jlms/s2-18.1.50
[16] C. SCHENSTED , Longest Increasing and Decreasing Subsequences (Canad. J. Math., Vol. 13, 1961 , pp. 179-191). MR 22 #12047 | Zbl 0097.25202 · Zbl 0097.25202 · doi:10.4153/CJM-1961-015-3
[17] R. STEINBERG , Lectures on Chevalley Groups , Yale University, 1967 . · Zbl 0164.34302
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.