Symmetric products, linear representations and the commuting scheme

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dc.creatorVaccarino, Francesco
dc.date2006-02-28
dc.date2007-06-08
dc.date.accessioned2026-07-07T08:07:36Z
dc.date.available2026-07-07T08:07:36Z
dc.descriptionWe show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting generic matrices. As a consequence we give a surjection from the ring of invariants of several matrices to the ring of multisymmetric functions generalizing a classical result of H.Weyl and F.Junker. We also find a surjection from the ring of invariants over the commuting scheme to the ring of multisymmetric functions. This surjection is an isomophism over a characteristic zero field and induces an isomorphism at the level of reduced structures over an infinite field of positive characteristic.
dc.descriptionAccepted for publication on "Journal of Algebra", Elsevier. 9 pages
dc.identifierhttps://arxiv.org/abs/math/0602660
dc.identifierhttp://arxiv.org/abs/math/0602660
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130986
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectRepresentation Theory
dc.subject14L30;13A50;14A15
dc.titleSymmetric products, linear representations and the commuting scheme
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