Maximal singular loci of Schubert varieties in SL(n)/B
Sara C. Billey, Gregory S. Warrington
Abstract
We give an explicit combinatorial description of the irreducible components of the singular locus of the Schubert variety Xw for any element w in Sn. Our description of the irreducible components is computationally more efficient (O(n6)) 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.
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