PBW Filtration and Bases for Symplectic Lie Algebras
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- 17 February 2011
- journal article
- research article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2011 (24) , 5760-5784
Abstract
We study the PBW filtration on the highest weight representations V (λ) of . This filtration is induced by the standard degree filtration on . We give a description of the associated graded -module gr V (λ) in terms of generators and relations. We also construct a basis of gr V (λ). As an application we derive a graded combinatorial formula for the character of V (λ) and obtain a new class of bases of the modules V (λ).Keywords
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