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28 March 2024
 
  » arxiv » 1302.3009

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Excited Young diagrams, equivariant K-theory, and Schubert varieties
William Graham ; Victor Kreiman ;
Date 13 Feb 2013
AbstractWe give combinatorial descriptions of the restrictions to T-fixed points of the classes of structure sheaves of Schubert varieties in the T-equivariant K-theory of Grassmannians and of maximal isotropic Grassmannians of orthogonal and symplectic types. We also give formulas, based on these descriptions, for the Hilbert series and Hilbert polynomials at T-fixed points of the corresponding Schubert varieties. These descriptions and formulas are given in terms of two equivalent combinatorial models: excited Young diagrams and set-valued tableaux. In types A_n and C_n the restriction formulas had been proved earlier by [Kreiman 05], [Kreiman 06] by a different method. In type A_n, the formula for the Hilbert series had been proved earlier by [Li-Yong 12]. The method of this paper, which relies on a restriction formula of [Graham 02] and [Willems 06], is based on the method used by [Ikeda-Naruse 09] to obtain the analogous formulas in equivariant cohomology. We also give Hilbert series and Hilbert polynomial formulas which are valid for Schubert varieties in any cominuscule flag variety, in terms of the 0-Hecke algebra.
Source arXiv, 1302.3009
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