$\mathcal{A}\mathcal{V}$ modules of finite type on affine space
Representation Theory
2020-02-21 v1
Abstract
We study the category of modules admitting compatible actions of the Lie algebra of vector fields on an affine space and the algebra of polynomial functions. We show that modules in this category which are finitely generated over , are free. We also show that this pair of compatible actions is equivalent to commuting actions of the algebra of differential operators and the Lie algebra of vector fields vanishing at the origin. This allows us to construct explicit realizations of such modules as gauge modules.
Cite
@article{arxiv.2002.08388,
title = {$\mathcal{A}\mathcal{V}$ modules of finite type on affine space},
author = {Yuly Billig and Colin Ingalls and Amir Nasr},
journal= {arXiv preprint arXiv:2002.08388},
year = {2020}
}