Symmetric coinvariant algebras and local Weyl modules at a double point

Details Symmetric coinvariant algebras and local Weyl modules at a double point Symmetric coinvariant algebras and local Weyl modules at a double point

2004-07-26

arxiv.org/abs/math/0407429v1

Mathematics

Representation Theory

13 pages

Scientific paper

The 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 $sl_{r+1} otimes A$.

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