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2005.52: Standard tableaux and Klyachko's Theorem on Lie representations

2005.52: Marianne Johnson (2005) Standard tableaux and Klyachko's Theorem on Lie representations. Journal of Combinatorial Theory, Series A. ISSN 1749-9097

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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 2000 > 05 CombinatoricsMSC 2000 > 17 Nonassociative rings and algebrasMSC 2000 > 20 Group theory and generalizations 2005.52 Dr Marianne Johnson 05 April 2006