Jack polynomials and Hilbert schemes of points on surfaces

dc.creatorNakajima, Hiraku
dc.date1996-10-31
dc.date.accessioned2026-07-07T09:07:02Z
dc.date.available2026-07-07T09:07:02Z
dc.descriptionThe 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.descriptionAMSLaTeXv1.2 + epic.sty + eepic.sty + youngtab.sty, 20pages
dc.identifierhttps://arxiv.org/abs/alg-geom/9610021
dc.identifierhttp://arxiv.org/abs/alg-geom/9610021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150224
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.subjectExactly Solvable and Integrable Systems
dc.subject14C05, 05E05
dc.titleJack polynomials and Hilbert schemes of points on surfaces
dc.typetext

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