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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
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representations of $S_k \times S_j$
For a group $G$ and a field $K$ let $S(G,K)$ be the sum of the dimensions of the irreducible K representations of $G$. Note that $S(G,\mathbb{C})< |G|$. It's not difficult to prove that if $n \ge 6$ t …