Symmetric coinvariant algebras and local Weyl modules at a double point

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dc.creatorKuwabara, Toshiro
dc.date2004-07-26
dc.date.accessioned2026-07-07T05:10:40Z
dc.date.available2026-07-07T05:10:40Z
dc.descriptionThe symmetric coinvariant algebra $C[x_1, dots, x_n]_{S_n}$ is the quotient algebra of the polynomial ring by the ideal generated by symmetric polynomials vanishing at the origin. It is known that the algebra is isomorphic to the regular representation of $S_n$. Replacing $C[x]$ with $A = C[x,y]/(xy)$, we introduce another symmetric coinvariant algebra $A^{otimes n}_{S_n}$ and determine its $S_n$-module structure. As an application, we determine the $sl_{r+1}$-module structure of the local Weyl module at a double point for $sl_{r+1} otimes A$.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0407429
dc.identifierhttp://arxiv.org/abs/math/0407429
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71998
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleSymmetric coinvariant algebras and local Weyl modules at a double point
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