  The polynomial ideals studied by A. Garsia and C. Procesi play an important
role in the theory of Kostka polynomials. We give multiparameter flat
deformations of these ideals and define an action of the extended affine
symmetric group on the corresponding quotient algebras multiplied by the sign
representation. We show that the images of these modules under the affine
Schur-Weyl duality are dual to the local Weyl modules for the loop algebra
$\mathfrak{sl}_{n+1}[t^{\pm 1}].$
