Geodesic
Lower bound on the dimensions or irreducible representations of symmetric groups and on the exponents of varieties of Lie algebras
Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 81-92 
S. P. Mishchenko. Lower bound on the dimensions or irreducible representations of symmetric groups and on the exponents of varieties of Lie algebras. Sbornik. Mathematics, Tome 187 (1996) no. 1, pp. 81-92. http://geodesic.mathdoc.fr/item/SM_1996_187_1_a4/
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     title = {Lower bound on the~dimensions or irreducible representations of symmetric groups and on the~exponents of varieties of {Lie} algebras},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two main results of this paper are singled out. The first one relates to the representation theory of symmetric groups. The second one deals with varieties of Lie algebras over a field of characteristic zero. The first result can be presented as follows: given a symmetric group of sufficiently large degree $n$, every irreducible representation of it with Young diagram fitting into a square with side $n/k$ is of dimension at least $k^n$. The second result states that there are no varieties of Lie algebras over a field of characteristic zero with lower exponent strictly less than two. At the same time, examples of varieties with exponent two are presented.

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