2013/10/11 by Mikhail A. Bochkarev, Bochkarev, Mikhail A., Mikhail V. Ignatyev +3 · 1 citation
Mathematics · #14M15 #20G20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14M15 #msc:20G20
paper · pdf · doi:10.48550/arxiv.1310.3166
18 pages. arXiv admin note: text overlap with arXiv:1210.5740 In the second version we add proofs of some new results
openalex publication_date 2013/10/11 · arxiv created 2015/01/12 · arxiv updated 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a complex reductive group, T be a maximal torus of G, B be a Borel subgroup of G containing T, W be the Weyl group of G with respect to T. To each element w of W one can associate the Schubert subvariety Xw of the flag variety G/B, the tangent cone to Xw at the identity point p considered as a subcheme of the tangent space Tp(G/B), and the reduced tangent cone to Xw at p considered as a subvariety of Tp(G/B). Let w1, w2 be distinct involutions in W. We prove that if G is of type Bn or Cn, then the tangent cones corresponding to w1 and w2 are distinct. We also prove that if G is of type An or Cn, then the reduced tangent cones corresponding to w1 and w2 are distinct.