English

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

Representation Theory 2007-05-23 v2 Quantum Algebra

Abstract

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 a connection between primitive ideals of U(g) attached to the nilpotent orbit containing e and finite-dimensional representations of the reduced enveloping algebra assiciated with e over an algebraically closed field of finite characteristic.

Keywords

Cite

@article{arxiv.math/0612465,
  title  = {Primitive ideals, non-restricted representations and finite W-algebras},
  author = {Alexander Premet},
  journal= {arXiv preprint arXiv:math/0612465},
  year   = {2007}
}

Comments

19 pages, minor corrections and up-dates, the new version is accepted for publication

R2 v1 2026-07-22T17:47:56.308Z