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
$\Sl \otimes A$.