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Questions about the branch of algebra that deals with groups.

24 votes
5 answers
3k views

Why are Jucys-Murphy elements' eigenvalues whole numbers?

The Jucys-Murphy elements of the group algebra of a finite symmetric group (here's the definition in Wikipedia) are known to correspond to operators diagonal in the Young basis of an irreducible repre …
13 votes

Why are Jucys-Murphy elements' eigenvalues whole numbers?

I came up with a more or less elementary proof of the identity from the top comment to my question. It involves nothing more advanced than some basic linear algebra. Namely, let us denote $X_k=\sum\l …
Igor Makhlin's user avatar
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