Paving Hessenberg varietes by affines

Details Paving Hessenberg varietes by affines Paving Hessenberg varietes by affines

2004-09-07

arxiv.org/abs/math/0409118v2

Mathematics

Algebraic Geometry

15 pages, v2: minor textual revisions

Scientific paper

Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising 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, generalizing results of de Concini-Lusztig-Procesi and Kostant. This paving is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties have no odd-dimensional homology.

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