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Background on representations of $\mathrm{sl}(3,\mathbb{C})$ In Chapter 6 of Brian C. Hall's book "Lie Groups, Lie Algebras, and Representations", he constructs the irreducible ...

Define a Lie bracket on the group algebra of the permutation group $S_n$ in the following way: $$[\sigma, \tau] = \sigma\circ\tau - \tau\circ\sigma,$$ where $\sigma, \tau \in S_n$, and the ...