Equivariant D-modules on binary cubic forms
Commutative Algebra
2017-12-29 v1 Algebraic Geometry
Representation Theory
Abstract
We consider the space X = Sym^3(C^2) of binary cubic forms, equipped with the natural action of the group GL_2 of invertible linear transformations of C^2. We describe explicitly the category of GL_2-equivariant coherent D_X-modules as the category of representations of a quiver with relations. We show moreover that this quiver is of tame representation type and we classify its indecomposable representations. We also give a construction of the simple equivariant D_X-modules (of which there are 14), and give formulas for the characters of their underlying GL_2-representations. We conclude the article with an explicit calculation of (iterated) local cohomology groups with supports given by orbit closures.
Cite
@article{arxiv.1712.09932,
title = {Equivariant D-modules on binary cubic forms},
author = {András C. Lőrincz and Claudiu Raicu and Jerzy Weyman},
journal= {arXiv preprint arXiv:1712.09932},
year = {2017}
}