Imposing Linear Conditions on Flag Varieties
نویسنده
چکیده
Abstract. We study subvarieties of the flag variety defined by certain linear conditions. These subvarieties are called Hessenberg varieties and arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(C) and show that they have no odd-dimensional homology. We provide an explicit geometric construction which partitions each Hessenberg variety into pieces homeomorphic to affine space. We also characterize these affine pieces by fillings of certain Young tableaux and show that the dimension of the affine piece can be computed by combinatorial rules. We give an equivalent formulation in terms of roots, and open questions about Hessenberg varieties.
منابع مشابه
Linear Conditions Imposed on Flag Varieties
We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(C) and show that they have no odd-dimensional homology. We provide an explicit geometr...
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