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11 votes
1 answer
550 views

Probability of words summing to $1$ in $S_n$ or $\mathrm{PGL}_2(n)$

$\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Conj{Conj}$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 ...
LeechLattice's user avatar
  • 9,501
3 votes
0 answers
400 views

Character table of the symmetric group $S_n$ according to James

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) $$\...
Stefan Witzel's user avatar
2 votes
0 answers
220 views

Characters of alternating groups

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_{...
dm82424's user avatar
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