منابع مشابه
Smooth Components of Springer Fibers
This article studies components of Springer fibers for gl(n) that are associated to closed orbits of GL(p) × GL(q) on the flag variety of GL(n), n = p+ q. These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the ...
متن کاملRegular Points in Affine Springer Fibers Mark Goresky, Robert Kottwitz, and Robert Macpherson
studied by Kazhdan and Lusztig in [KL88]. For x = gG(O) ∈ X the G(O)-orbit (for the adjoint action) of Ad(g)(u) in g(O) depends only on x, and its image under g(O) ։ g(C) is a well-defined G(C)orbit in g(C). We say that x ∈ X is regular if the associated orbit is regular in g(C). (Recall that an element of g(C) is regular if the nilpotent part of its Jordan decomposition is a principal nilpoten...
متن کاملPurity of Equivalued Affine Springer Fibers
The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its homology is “pure”.
متن کاملHomology of Affine Springer Fibers in the Unramified Case
Assuming a certain “purity” conjecture, we derive a formula for the (complex) cohomology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the “kappa” orbital integral that arises in the fundamental lemma is equal to the Lefschetz trace of ...
متن کاملIntegral Points on Generic Fibers
Let P (x, y) be a rational polynomial. If the curve (P (x, y) = k), k ∈ Q, is irreducible and admits an infinite number of points whose coordinates are integers, Siegel’s theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar-MohSuzuki theorem, that there exists an algebraic automorphism sending P (x, y) to the poly...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.08.010