A note on Verma modules for finite W-algebras

作者：Goodwin Simon M^*

来源：Journal of Algebra, 2010, 324(8): 2058-2063.

DOI：10.1016/j.jalgebra.2010.06.027

• Finite W-algebras

A finite W-algebra U(g, e) is a certain finitely generated algebra associated to a nilpotent element e of a complex reductive Lie algebra g. There is a (loop) filtration on U(g, e) such that the associated graded algebra is isomorphic to U(g(e)), where g(e) is the centralizer of e in g. In this short note, we show that Verma modules for finite W-algebras, as defined in Brundan et al. (2008) [BGK] are filtered deformations of Verma modules for U(g(e)).

• 出版日期2010-10-15