Equivariant cohomology of incidence Hilbert schemes and loop algebras
| dc.creator | Li, Wei-Ping | |
| dc.creator | Qin, Zhenbo | |
| dc.date | 2008-02-12 | |
| dc.date.accessioned | 2026-07-07T09:20:16Z | |
| dc.date.available | 2026-07-07T09:20:16Z | |
| dc.description | Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct sum $$\Wft = \bigoplus_{m=0}^{+\infty}H^{2(m+1)}_{\mathbb T}(S^{[m,m+1]})$$ of the middle-degree equivariant cohomology group of $\hil{m,m+1}$. The algebra is related to the loop algebra of an infinite dimensional Heisenberg algebra. In addition, we study the transformations among three different linear bases of $\Wft$. Our results are applied to the ring structure of the ordinary cohomology of $\hil{m,m+1}$ and to the ring of symmetric functions in infinitely many variables. | |
| dc.description | 30 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0802.1673 | |
| dc.identifier | http://arxiv.org/abs/0802.1673 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154670 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14C05; 14F43, 17B65 | |
| dc.title | Equivariant cohomology of incidence Hilbert schemes and loop algebras | |
| dc.type | text |