Selecta Mathematica

, 13:353

Paving Hessenberg varieties by affines


DOI: 10.1007/s00029-007-0038-4

Cite this article as:
Tymoczko, J.S. Sel. math., New ser. (2007) 13: 353. doi:10.1007/s00029-007-0038-4


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).



Hessenberg varietiespavingBruhat decomposition

Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA