2014/10/15 by Mkhail V. Ignatyev, Ignatyev, Mkhail V., Aleksandr A. Shevchenko +1
Mathematics · #14M15 #20G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14M15 #msc:20G20
paper · pdf · doi:10.48550/arxiv.1410.4025
15 pages. arXiv admin note: substantial text overlap with arXiv:1310.3166
arxiv created 2014/10/15 · arxiv updated 2014/10/16
Let G be a complex reductive algebraic group, T a maximal torus in G, B a Borel subgroup of G containing T, W the Weyl group of G with respect to T. Let w be an element of W. Denote by Xw the Schubert subvariety of the flag variety G/B corresponding to w. Let Cw be the tangent cone to Xw at the point p=eB (we consider Cw as a subscheme of the tangent space to G/B at p). In 2011, D.Yu. Eliseev and A.N. Panov computed all tangent cones for G=SL(n), n<6. Using their computations, A.N. Panov formulated the following Conjecture: if w, w' are distinct involutions in W, then Cw and Cw' do not coincide. In 2013, D.Yu. Eliseev and the first author proved this conjecture in types An, F4 and G2. Later M.A. Bochkarev and the authors proved this conjecture in types Bn and Cn. In this paper we prove the conjecture in type Dn in the case when w, w' are basic involutions.