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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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DOI: 10.1016/j.jcta.2006.02.002


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
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Uncontrolled Keywords:standard tableau, free Lie algebra, Lie representation
Subjects:MSC 2000 > 05 Combinatorics
MSC 2000 > 17 Nonassociative rings and algebras
MSC 2000 > 20 Group theory and generalizations
MIMS number:2005.52
Deposited By:Dr Marianne Johnson
Deposited On:05 April 2006

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