Jack polynomials and Hilbert schemes of points on surfaces
| dc.creator | Nakajima, Hiraku | |
| dc.date | 1996-10-31 | |
| dc.date.accessioned | 2026-07-07T09:07:02Z | |
| dc.date.available | 2026-07-07T09:07:02Z | |
| dc.description | The Jack symmetric polynomials $P_λ^{(α)}$ form a class of symmetric polynomials which are indexed by a partition $λ$ and depend rationally on a parameter $α$. They reduced to the Schur polynomials when $α=1$, and to other classical families of symmetric polynomials for several specific parameters. It is well-known that Schur polynomials can be realized as certain elements of homology groups of Grassmann manifolds. The purpose of this paper is to give a similar geometric realization for Jack polynomials. However, spaces which we use are totally different. Our spaces are Hilbert schemes of points on a surface X which is the total space of a line bundle L over the projective line. The parameter $α$ in Jack polynomials relates to our surface X by $α= -<C,C>$, where C is the zero section, and <C,C> is the self-intersection number of C. | |
| dc.description | AMSLaTeXv1.2 + epic.sty + eepic.sty + youngtab.sty, 20pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9610021 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9610021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150224 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 14C05, 05E05 | |
| dc.title | Jack polynomials and Hilbert schemes of points on surfaces | |
| dc.type | text |