Irreducible Highest Weight Representations Of The Simple n-Lie Algebra

2010/11/30 by Dana Balibanu, Johan van de Leur · 1 citation
Mathematics · Physics and Astronomy · #math.RT #hep-th #math-ph #math.MP #msc:17B10 #msc:17B99

paper · pdf · doi:10.1007/s00031-012-9189-2

published as Transformation Groups, Vol 17, No 3, 2012, pp 593-613 · 24 pages, 24 figures, mistake in proposition 2.1 corrected

arxiv created 2015/12/11 · arxiv updated 2015/12/14

Abstract

A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra.

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