The University of Michigan Combinatorics Seminar
In 1984, Lakshmibai & Seshadri gave a combinatorial criterion for a point to be in the singular locus of a Schubert variety X_w in Sl(n)/B. Such points comprise a union of lower order ideals. Using the criterion of Lakshmibai & Seshadri, Sara Billey and I have found an explicit combinatorial description of the maximal elements in this singular locus. We also refine the 1990 work of Lakshmibai & Sandhya that expresses the singularity of a Schubert variety in terms of the patterns 3412 and 4231. In fact, the maximal singular points are obtained by acting on w by cycles corresponding to generalizations of the 3412 and 4231 patterns.