A note on Verma modules for finite W-algebras

Simon Goodwin

doi:10.1016/j.jalgebra.2010.06.027

A note on Verma modules for finite W-algebras

Simon Goodwin

Mathematics

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Abstract

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)). (C) 2010 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	2058-2063
Number of pages	6
Journal	Journal of Algebra
Volume	324
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2010.06.027
Publication status	Published - 15 Oct 2010

Keywords

Finite W-algebras

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10.1016/j.jalgebra.2010.06.027

Representation Theory of Finite W-algebras
Goodwin, S. (Principal Investigator)
Engineering & Physical Science Research Council
17/08/09 → 16/08/12
Project: Research Councils

Cite this

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AB - 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)). (C) 2010 Elsevier Inc. All rights reserved.

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DO - 10.1016/j.jalgebra.2010.06.027

M3 - Article

VL - 324

SP - 2058

EP - 2063

JO - Journal of Algebra

JF - Journal of Algebra

IS - 8

ER -

A note on Verma modules for finite W-algebras

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Keywords

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Representation Theory of Finite W-algebras

Cite this