2001/08/31 by Georgia Benkart, Stephen Doty
Mathematics · #math.RT #math.CO #msc:17B10
published as Journal of Algebraic Combinatorics 16 (2002), 31-42 · This is a revised version of a paper by the same title that appeared in Journal of Algebraic Combinatorics 16 (2002), 31-42. In particular 1.15-1.18 in that paper have been revised in 1.15-1.18 here and a few other related minor changes have been made in the first line of Section 2 and in Section 3. We are grateful to Alberto Elduque for alerting us to the mistake in the previous version
We obtain the decomposition of the tensor space \mathfraksln⊗ k as a module for \mathfraksln, find an explicit formula for the multiplicities of its irreducible summands, and (when n ≥ 2k) describe the centralizer algebra C=End_\mathfraksln(\mathfraksln⊗ k) 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.