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Questions about the branch of algebra that deals with groups.

2 votes

Generalization of Schur's lemma (Update)

I'm afraid I do not know the answer to your problem, but here's a counterexample to your conjecture that the result is zero if $r'\ne r''$. take $r=(2,1)$ (i.e., the Young diagram with two boxes one t …
Paul Zinn-Justin's user avatar
5 votes
Accepted

transposing "unrimmed" permutations

The answer is $a_n=8(n-2)!$ for $n\ge 4$. Subdivide into cases depending on the values at corners and count. (6 cases give 1, 1 case gives 2 times $(n-2)!$)
Paul Zinn-Justin's user avatar