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)

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.