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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn051, 53 pages, doi:10.1093/imrn/rnn051 published on May 22, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Highest Weight Theory for Finite W-Algebras

Jonathan Brundan1, Simon M. Goodwin2 and Alexander Kleshchev1

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
2 School of Mathematics, University of Birmingham, Birmingham, B15 3LX, UK

Correspondence: Correspondence to be sent to: klesh{at}uoregon.edu

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 Formula . 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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