Title: Symmetric coinvariant algebra and local Weyl module at a double point Author: Toshiro Kuwabara (Kyoto Univ.) Abstract: The symmetric coinvariant algebra $\C[x_1, \dots, x_n]/\langle \C[x_1, \dots, x_n]^{S_n}_{+} \rangle$ is defined as the quotient algebra of the polynomial ring by the ideal generated by symmetric polynomials vanishing at the origin. Classically, 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 $A^{\otimes n}/\langle (A^{\otimes n})^{S_n}_{+} \rangle$ and determine its $S_n$-module structure. As a corollary, we calculate the dimension of the local Weyl module at a double point for $\Sl \otimes A$.