Decomposing Hessenberg varieties over classical groups
| dc.creator | Tymoczko, Julianna S. | |
| dc.date | 2002-11-14 | |
| dc.date | 2004-09-05 | |
| dc.date.accessioned | 2026-07-07T04:52:56Z | |
| dc.date.available | 2026-07-07T04:52:56Z | |
| dc.description | Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from a problem in numerical analysis and consists for a fixed linear operator M of the full flags V_1 \subsetneq V_2 >... \subsetneq V_n in GL_n with M V_i contained in V_{i+1} for all i. In this paper I show that all Hessenberg varieties in type A_n and semisimple and regular nilpotent Hessenberg varieties in types B_n,C_n, and D_n can be paved by affine spaces. Moreover, this paving is the intersection of a particular Bruhat decomposition with the Hessenberg variety. In type A_n, an equivalent description of the cells of the paving in terms of certain fillings of a Young diagram can be used to compute the Betti numbers of Hessenberg varieties. As an example, I show that the Poincare polynomial of the Peterson variety in A_n is \sum_{i =0}^{n-1} \binom{n-1}{i} x^{2i}. | |
| dc.description | 27 pages; v2 is final version of author's Ph.D. thesis | |
| dc.identifier | https://arxiv.org/abs/math/0211226 | |
| dc.identifier | http://arxiv.org/abs/math/0211226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65657 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 20G20 (Primary) 05E10, 20G10 (Secondary) | |
| dc.title | Decomposing Hessenberg varieties over classical groups | |
| dc.type | text |