2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60982We give an explicit combinatorial description of the irreducible components of the singular locus of the Schubert variety X_w for any element w in S_n. Our description of the irreducible components is computationally more efficient (O(n^6)) than the previously best known algorithms. This result proves a conjecture of Lakshmibai and Sandhya regarding this singular locus. Furthermore, we give simple formulas for calculating the Kazhdan-Lusztig polynomials at the maximum singular points.50 pages, 50 figuresAlgebraic GeometryCombinatorics14M15; 05E15text