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The PBW filtration

Author(s): Evgeny Feigin
Journal: Represent. Theory 13 (2009), 165-181.
MSC (2000): Primary 17B67, 81R10
Posted: May 1, 2009
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Abstract: In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras $ \widehat{\mathfrak{g}}$. The $ n$-th space of this filtration is spanned by the vectors $ x_1\dots x_s v$, where $ x_i\in\widehat{\mathfrak{g}}$, $ s\le n$, and $ v$ is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. For $ \mathfrak{g}$ of the type $ A_1$ we prove our conjecture and derive the fermionic formula for the graded character.

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Additional Information:

Evgeny Feigin
Affiliation: Tamm Theory Division, Lebedev Physics Institute, Russian Academy of Sciences, Russia, 119991, Moscow, Leninski prospect, 53 - and - {\it Independent University of Moscow, Russia, Moscow, 119002, Bol'shoi Vlas'evskii, 11}
Email: evgfeig@gmail.com

DOI: 10.1090/S1088-4165-09-00349-5
PII: S 1088-4165(09)00349-5
Received by editor(s): November 15, 2007
Received by editor(s) in revised form: February 4, 2009
Posted: May 1, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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