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Can we relate the character of the permutation representation of $G$ on the cosets $G/\langle g_i\rangle$ to the number of cycles of $g_i$?

The Hurwitz representation's existence implies the inequality $(s-2) n - \sum_i c_i + 2\geq 0$ in general - there is no need to restrict to the case of $G$ acting on itself. If $G$ acts transitively ...
Will Sawin's user avatar
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4 votes

The sum (with multiplicity) of the cubes of irreducible character degrees of a finite group

It turns out that my original question does indeed have a positive answer. In fact, one can show that if $G$ has an irreducible character of degree $\geq 3$ then ${\rm AD}(G) \geq 2+ |G'|^{-1}$. The ...
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Chevalley restriction theorem

$\DeclareMathOperator\Sym{Sym}\DeclareMathOperator\trace{trace}$I can write the details of Humphreys' argument: For each integer $k\geq 1$ it suffices to show that the map $\theta:\Sym^k({\mathfrak g}^...
F Zaldivar's user avatar
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