Positivity of Equivariant Schubert Classes Through Moment Map Degeneration
| dc.creator | Zara, Catalin | |
| dc.date | 2009-04-06 | |
| dc.date.accessioned | 2026-07-07T13:00:49Z | |
| dc.date.available | 2026-07-07T13:00:49Z | |
| dc.description | For a flag manifold $M=G/B$ with the canonical torus action, the $T-$equivariant cohomology is generated by equivariant Schubert classes, with one class $τ_u$ for every element $u$ of the Weyl group $W$. These classes are determined by their restrictions to the fixed point set $M^T \simeq W$, and the restrictions are polynomials with nonnegative integer coefficients in the simple roots. The main result of this article is a positive formula for computing $τ_u(v)$ in types A, B, and C. To obtain this formula we identify $G/B$ with a generic co-adjoint orbit and use a result of Goldin and Tolman to compute $τ_u(v)$ in terms of the induced moment map. Our formula, given as a sum of contributions of certain maximal ascending chains from $u$ to $v$, follows from a systematic degeneration of the moment map, corresponding to degenerating the co-adjoint orbit. In type A we prove that our formula is manifestly equivalent to the formula announced by Billey in \cite{Bi}, but in type C, the two formulas are not equivalent. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0904.0902 | |
| dc.identifier | http://arxiv.org/abs/0904.0902 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225963 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Positivity of Equivariant Schubert Classes Through Moment Map Degeneration | |
| dc.type | text |