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I am studying certain properties of characters of alternating groups and I have found precisely three characters not satisfying it up to $A_{15}$. These are: A character of dimension $3.696$ of $A_{...

$\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Conj{Conj}$Let $G$ be the symmetric group $S_n$ or the projective general linear group $\PGL_2(n)$. Let $X$ be a cyclically reduced word in the ...

In James, "The representation theory of the symmetric groups" an algorithm is described to produce the character table of a symmetric group. The proof involves the equation (pp. 22,23) $$\...