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Excited Young diagrams, equivariant K-theory, and Schubert varieties | William Graham
; Victor Kreiman
; | Date: |
13 Feb 2013 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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