Derangements and tensor powers of adjoint modules for sl_n
We obtain the decomposition of the tensor space sl ⊗k n as a module for sln, find an explicit formula for the multiplicities of its irreducible summands, and (when n ≥ 2k) describe the centralizer algebra C = Endsln (sl ⊗k n ) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of C is given by the number of derangements of a set of 2k elements.