# Standard tableaux and Klyachko's Theorem on Lie representations

Johnson, Marianne (2005) Standard tableaux and Klyachko's Theorem on Lie representations. Journal of Combinatorial Theory, Series A. ISSN 1749-9097 (In Press)

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## Abstract

We show that for all but two partitions $\lambda$ of $n >6$ there exists a standard tableau of shape $\lambda$ with major index coprime to $n$. In conjunction with a deep result of Kra{\'s}kiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group.

Item Type: Article The full article can be accessed from the journals webpage http://www.sciencedirect.com/science/journal/00973165 standard tableau, free Lie algebra, Lie representation MSC 2010, the AMS's Mathematics Subject Classification > 05 CombinatoricsMSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebrasMSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations Dr Marianne Johnson 05 Apr 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/201

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