Multiplicative formulas in Cohomology of $G/P$ and in quiver representations
| dc.creator | Ressayre, Nicolas | |
| dc.date | 2008-12-11 | |
| dc.date.accessioned | 2026-07-07T12:11:59Z | |
| dc.date.available | 2026-07-07T12:11:59Z | |
| dc.description | Consider a partial flag variety $X$ which is not a grassmaninan. Consider also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the Poincaré dual classes of the Schubert varieties. In \cite{Richmond:recursion}, E. Richmond showed that some coefficient structure of the product in ${\rm H}^*(X,\ZZ)$ are products of two such coefficients for smaller flag varieties. Consider now a quiver without oriented cycle. If $α$ and $β$ denote two dimension-vectors, $α\circβ$ denotes the number of $α$-dimensional subrepresentations of a general $α+β$-dimensional representation. In \cite{DW:comb}, H. Derksen and J. Weyman expressed some numbers $α\circβ$ as products of two smaller such numbers. The aim of this work is to prove two generalisations of the two above results by the same way. | |
| dc.description | The main result of this note was obtained simultenously by E. Richmond (see arXiv:0812.1856) | |
| dc.identifier | https://arxiv.org/abs/0812.2122 | |
| dc.identifier | http://arxiv.org/abs/0812.2122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210399 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Multiplicative formulas in Cohomology of $G/P$ and in quiver representations | |
| dc.type | text |