Idempotents for derangement numbers (Q1402079)

The principal result of this paper locates a set of orthogonal idempotents in Solomon's descent algebra. The representations of the symmetric group arising from these idempotents have dimensions which are equal to the number of permutations with a particular number of fixed points. Connections with higher Lie representations are then demonstrated. Finally, a number of known results, including a well-known formula for \(q\)-derangement numbers, are rederived.