The singular locus of a Schubert variety

The singular locus of a Schubert variety Xμ in the flag variety for GLn(C) is the union of Schubert varieties Xν, where ν runs over a set Sg(μ) of permutations in Sn. We describe completely the maximal elements of Sg(μ) under the Bruhat order, thus determining the irreducible components of the singular locus of Xμ.