Paving Hessenberg Varieties by Affines

Authors

Julianna S. Tymoczko, University of IowaFollow

Document Type

Article

Publication Date

9-1-2007

Publication Title

Selecta Mathematica, New Series

Abstract

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.

Keywords

Bruhat decomposition, Hessenberg varieties, Paving

Volume

13

Issue

2

First Page

353

Last Page

367

DOI

10.1007/s00029-007-0038-4

ISSN

10221824

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Tymoczko, Julianna S., "Paving Hessenberg Varieties by Affines" (2007). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/109