Verma module annihilators for quantized enveloping algebras
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 28 (1995) no. 4, p. 493-526
@article{ASENS_1995_4_28_4_493_0,
     author = {Joseph, Anthony and Letzter, Gail},
     title = {Verma module annihilators for quantized enveloping algebras},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 28},
     number = {4},
     year = {1995},
     pages = {493-526},
     doi = {10.24033/asens.1723},
     zbl = {0838.17011},
     mrnumber = {96i:17011},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1995_4_28_4_493_0}
}
Joseph, Anthony; Letzter, Gail. Verma module annihilators for quantized enveloping algebras. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 28 (1995) no. 4, pp. 493-526. doi : 10.24033/asens.1723. http://www.numdam.org/item/ASENS_1995_4_28_4_493_0/

[B] W. Borho, On the Joseph-Small additivity principle for Goldie ranks (Compos. Math., Vol. 43, 1982, pp. 3-29). | Numdam | MR 84a:17007 | Zbl 0502.17007

[BK] W. Borho and H. Kraft, Über die Gelfand-Kirillov-Dimension (Math. Ann., Vol. 220, 1976, pp. 1-24). | MR 54 #367 | Zbl 0306.17005

[Bo] N. Bourbaki, Commutative algebra, Springer-Verlag, Berlin, 1980.

[D] J. Dixmier, Algèbres enveloppantes, cahiers scientifiques no. 37, Gauthier-Villars, Paris, 1974. | MR 58 #16803a | Zbl 0308.17007

[DeC-K] C. De Concini and V. Kac, Representations of quantum groups at roots of 1 (In Progress in Math., Vol. 92 (Ed. A. Connes et al.) Birkhauser, Boston, 1990, pp. 471-506). | MR 92g:17012 | Zbl 0738.17008

[Dr] V. G. Drinfeld, On some unsolved problems in quantum group theory (In Quantum Groups, Ed. P.P. Kulish, LN 1510 Springer-Verlag, Berlin, 1992). | MR 94a:17006 | Zbl 0765.17014

[H] I. N. Herstein, Topics in Ring Theory, Chicago Press, Chicago, 1969. | MR 42 #6018 | Zbl 0232.16001

[He] W. H. Hesselink, Characters of the Nullcone (Math. Ann., Vol. 252, 1980, pp. 179-182). | MR 82c:17004 | Zbl 0447.17006

[J1] A. Joseph, The primitive spectrum of an enveloping algebra (Astérisque, Vol. 173-174, 1989, pp. 13-53). | MR 91b:17012 | Zbl 0714.17011

[J2] A. Joseph, Enveloping algebras : Problems old and new. (In Progress in Math., Vol. 123, Birkhäuser, Boston, 1994, pp. 385-413). | MR 96e:17022 | Zbl 0847.17007

[J3] A. Joseph, A generalization of the Gelfand-Kirillov conjecture (Amer. J. Math., Vol. 99, 1977, pp. 1151-1165). | MR 57 #391 | Zbl 0378.17005

[Ja] J.-C. Jantzen, Moduln mit einem höchsten Gewicht, LN 750, Springer-Verlag, Heidelberg, 1979. | MR 81m:17011 | Zbl 0426.17001

[JL1] A. Joseph and G. Letzter, Local finiteness of the adjoint action for quantized enveloping algebras (J. Algebra, Vol. 153, 1992, pp. 289-318). | MR 94b:17023 | Zbl 0779.17012

[JL2] A. Joseph and G. Letzter, Separation of variables for quantized enveloping algebras. | Zbl 0811.17007

[K] B. Kostant, On the existence and irreducibility of certain series of representations (Bull. Amer. Math. Soc., Vol. 75, 1969, pp. 627-642). | MR 39 #7031 | Zbl 0229.22026

[KL] G. B. Krause and T. H. Lenagen, Growth of algebras and Gelfand-Kirillov dimension (Research Notes in Math., Vol. 116, Pitman, London, 1985). | MR 86g:16001 | Zbl 0564.16001

[L] G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras (Adv. Math., Vol. 70, 1988, pp. 237-249). | MR 89k:17029 | Zbl 0651.17007

[M] J. C. Mcconnell, Quantum groups, filtered rings and Gelfand-Kirillov dimension. (In Lecture Notes in Math., Vol. 1448, Springer, Berlin, 1991, pp. 139-149). | MR 91j:17020 | Zbl 0717.17016

[PRV] K. R. Parthasarathy, R. Ranga Rao and V. S. Varaderajan, Representations of complex semi-simple Lie groups and Lie algebras (Annals of Math., Vol. 85, 1967, pp. 383-429). | MR 37 #1526 | Zbl 0177.18004

[R1] M. Rosso, Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra (Comm. Math. Phys., Vol. 117, 1988, pp. 581-593). | MR 90c:17019 | Zbl 0651.17008

[R2] M. Rosso, Analogues de la forme de Killing et du théorème de Harish-Chandra pour les groupes quantiques (Ann. Sc. Ec. Norm. Sup., Vol. 23, 1990, pp. 445-467). | Numdam | MR 93e:17026 | Zbl 0721.17012

[S] R. Steinberg, On a theorem of Pittie (Topology, Vol. 14, 1975, pp. 173-7). | MR 51 #9101 | Zbl 0318.22010