Selecta Mathematica

, Volume 13, Issue 2, pp 353-367

First online:

Paving Hessenberg varieties by affines

  • Julianna S. TymoczkoAffiliated withDepartment of Mathematics, University of Iowa Email author 

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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.

Mathematics Subject Classification (2000).

14M15 14F25 14L35


Hessenberg varieties paving Bruhat decomposition