Maximal singular loci of Schubert varieties in SL(n)/B

2001/02/21 by Sara Billey, Sara C. Billey, Billey, Sara C. +2
Mathematics · #05E15 #14M15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:05E15 #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/0102168

50 pages, 50 figures

arxiv created 2001/02/21 · openalex publication_date 2001/02/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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(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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