Paving Hessenberg Varieties by Affines
نویسنده
چکیده
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety which arise in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types. This paving is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of this paving and their dimensions can be identified by a combinatorial condition on roots. We use this paving to prove these Hessenberg varieties have no odd-dimensional homology.
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