Verma module annihilators for quantized enveloping algebras

Anthony Joseph; Gail Letzter

Annales scientifiques de l'École Normale Supérieure (1995)

  • Volume: 28, Issue: 4, page 493-526
  • ISSN: 0012-9593

How to cite

top

Joseph, Anthony, and Letzter, Gail. "Verma module annihilators for quantized enveloping algebras." Annales scientifiques de l'École Normale Supérieure 28.4 (1995): 493-526. <http://eudml.org/doc/82392>.

@article{Joseph1995,
author = {Joseph, Anthony, Letzter, Gail},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {quantized enveloped algebra; Verma module; annihilator; separation of variables},
language = {eng},
number = {4},
pages = {493-526},
publisher = {Elsevier},
title = {Verma module annihilators for quantized enveloping algebras},
url = {http://eudml.org/doc/82392},
volume = {28},
year = {1995},
}

TY - JOUR
AU - Joseph, Anthony
AU - Letzter, Gail
TI - Verma module annihilators for quantized enveloping algebras
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1995
PB - Elsevier
VL - 28
IS - 4
SP - 493
EP - 526
LA - eng
KW - quantized enveloped algebra; Verma module; annihilator; separation of variables
UR - http://eudml.org/doc/82392
ER -

References

top
  1. [B] W. BORHO, On the Joseph-Small additivity principle for Goldie ranks (Compos. Math., Vol. 43, 1982, pp. 3-29). Zbl0502.17007MR84a:17007
  2. [BK] W. BORHO and H. KRAFT, Über die Gelfand-Kirillov-Dimension (Math. Ann., Vol. 220, 1976, pp. 1-24). Zbl0306.17005MR54 #367
  3. [Bo] N. BOURBAKI, Commutative algebra, Springer-Verlag, Berlin, 1980. 
  4. [D] J. DIXMIER, Algèbres enveloppantes, cahiers scientifiques no. 37, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR58 #16803a
  5. [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). Zbl0738.17008MR92g:17012
  6. [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). Zbl0765.17014MR94a:17006
  7. [H] I. N. HERSTEIN, Topics in Ring Theory, Chicago Press, Chicago, 1969. Zbl0232.16001MR42 #6018
  8. [He] W. H. HESSELINK, Characters of the Nullcone (Math. Ann., Vol. 252, 1980, pp. 179-182). Zbl0447.17006MR82c:17004
  9. [J1] A. JOSEPH, The primitive spectrum of an enveloping algebra (Astérisque, Vol. 173-174, 1989, pp. 13-53). Zbl0714.17011MR91b:17012
  10. [J2] A. JOSEPH, Enveloping algebras : Problems old and new. (In Progress in Math., Vol. 123, Birkhäuser, Boston, 1994, pp. 385-413). Zbl0847.17007MR96e:17022
  11. [J3] A. JOSEPH, A generalization of the Gelfand-Kirillov conjecture (Amer. J. Math., Vol. 99, 1977, pp. 1151-1165). Zbl0378.17005MR57 #391
  12. [Ja] J.-C. JANTZEN, Moduln mit einem höchsten Gewicht, LN 750, Springer-Verlag, Heidelberg, 1979. Zbl0426.17001MR81m:17011
  13. [JL1] A. JOSEPH and G. LETZTER, Local finiteness of the adjoint action for quantized enveloping algebras (J. Algebra, Vol. 153, 1992, pp. 289-318). Zbl0779.17012MR94b:17023
  14. [JL2] A. JOSEPH and G. LETZTER, Separation of variables for quantized enveloping algebras. Zbl0811.17007
  15. [K] B. KOSTANT, On the existence and irreducibility of certain series of representations (Bull. Amer. Math. Soc., Vol. 75, 1969, pp. 627-642). Zbl0229.22026MR39 #7031
  16. [KL] G. B. KRAUSE and T. H. LENAGEN, Growth of algebras and Gelfand-Kirillov dimension (Research Notes in Math., Vol. 116, Pitman, London, 1985). Zbl0564.16001MR86g:16001
  17. [L] G. LUSZTIG, Quantum deformations of certain simple modules over enveloping algebras (Adv. Math., Vol. 70, 1988, pp. 237-249). Zbl0651.17007MR89k:17029
  18. [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). Zbl0717.17016MR91j:17020
  19. [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). Zbl0177.18004MR37 #1526
  20. [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). Zbl0651.17008MR90c:17019
  21. [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). Zbl0721.17012MR93e:17026
  22. [S] R. STEINBERG, On a theorem of Pittie (Topology, Vol. 14, 1975, pp. 173-7). Zbl0318.22010MR51 #9101

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.