Commutative quotients of finite W-algebras
Representation Theory
2008-09-15 v2 Rings and Algebras
Abstract
Let U(g,e) be the finite W-algebra associated with a nilpotent element e in a simple Lie algebra g and assume that e is induced from a nilpotent element e_0 in a Levi subalgebra l of g. We show that if the finite W-algebra U(l,e_0) has a 1-dimensional representation, then so does U(g,e). For g classical (and in may other cases), we compute the Krull dimension of the largest commutative quotient of U(g,e). Some applications to representation theory of modular counterparts of g are given.
Keywords
Cite
@article{arxiv.0809.0663,
title = {Commutative quotients of finite W-algebras},
author = {Alexander Premet},
journal= {arXiv preprint arXiv:0809.0663},
year = {2008}
}
Comments
35 pages; one subsection added, some typos corrcted