Primitive ideals, non-restricted representations and finite W-algebras

作者: A. Premet

DOI: 10.17323/1609-4514-2007-7-4-743-762

关键词:

摘要: We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish connection between primitive ideals of U(g) attached the orbit containing and representations reduced enveloping assiciated over an algebraically closed field characteristic.

参考文章(12)
Jens Carsten Jantzen, Karl-Hermann Neeb, Jens Carsten Jantzen, Nilpotent Orbits in Representation Theory Lie Theory. pp. 1- 211 ,(2004) , 10.1007/978-0-8176-8192-0_1
Wee Gan, Victor Ginzburg, Quantization of Slodowy slices International Mathematics Research Notices. ,vol. 2002, pp. 243- 255 ,(2002) , 10.1155/S107379280210609X
Alexander Premet, Nilpotent orbits in good characteristic and the Kempf–Rousseau theory Journal of Algebra. ,vol. 260, pp. 338- 366 ,(2003) , 10.1016/S0021-8693(02)00662-2
Alexander Premet, Enveloping algebras of Slodowy slices and the Joseph ideal Journal of the European Mathematical Society. ,vol. 9, pp. 487- 543 ,(2007) , 10.4171/JEMS/86
Jonathan Brundan, Alexander Kleshchev, Shifted Yangians and finiteW-algebras Advances in Mathematics. ,vol. 200, pp. 136- 195 ,(2006) , 10.1016/J.AIM.2004.11.004
Dan Barbasch, David Vogan, Primitive ideals and orbital integrals in complex exceptional groups Journal of Algebra. ,vol. 80, pp. 350- 382 ,(1983) , 10.1016/0021-8693(83)90006-6
Alexander Premet, Special transverse slices and their enveloping algebras Advances in Mathematics. ,vol. 170, pp. 1- 55 ,(2002) , 10.1006/AIMA.2001.2063
Dan Barbasch, David Vogan, Primitive ideals and orbital integrals in complex classical groups Mathematische Annalen. ,vol. 259, pp. 153- 199 ,(1982) , 10.1007/BF01457308
Victor Ginzburg, On primitive ideals Selecta Mathematica-new Series. ,vol. 9, pp. 379- 407 ,(2003) , 10.1007/S00029-003-0338-2
Anthony Joseph, On the variety of a highest weight module Journal of Algebra. ,vol. 88, pp. 238- 278 ,(1984) , 10.1016/0021-8693(84)90100-5