Highest Weight Theory for Finite W-Algebras

J Brundan; Simon Goodwin; A Kleshchev

doi:10.1093/imrn/rnn051

Highest Weight Theory for Finite W-Algebras

J Brundan, Simon Goodwin, A Kleshchev

Mathematics

Research output: Contribution to journal › Article

29 Citations (Scopus)

Abstract

We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step toward the classification of finite-dimensional irreducible modules. We also introduce an analogue of the BGG category O. Motivated by known results in type A, we then formulate some precise conjectures in the case of nilpotent orbits of standard Levi type.

Original language	English
Pages (from-to)	1-53
Number of pages	53
Journal	International Mathematics Research Notices
Volume	2008
Issue number	1
DOIs	https://doi.org/10.1093/imrn/rnn051
Publication status	Published - 8 Jul 2008

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10.1093/imrn/rnn051

Verma Modules for Finite W-algebras
Goodwin, S.
Engineering & Physical Science Research Council
7/06/07 → 6/10/07
Project: Research Councils

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AB - We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step toward the classification of finite-dimensional irreducible modules. We also introduce an analogue of the BGG category O. Motivated by known results in type A, we then formulate some precise conjectures in the case of nilpotent orbits of standard Levi type.

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Highest Weight Theory for Finite W-Algebras

Abstract

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Verma Modules for Finite W-algebras

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