On categories of equivariant D-modules

Add time:08/31/2019    Source:sciencedirect.com

Let X be a variety with an action by an algebraic group G. In this paper we discuss various properties of G-equivariant D-modules on X, such as the decompositions of their global sections as representations of G (when G is reductive), and descriptions of the categories that they form. When G acts on X with finitely many orbits, the category of equivariant D-modules is equivalent to the category of finite-dimensional representations of a finite quiver with relations. We describe explicitly these categories for irreducible G-modules X that are spherical varieties, and show that in such cases the quivers are almost always representation-finite (i.e. with finitely many indecomposable representations).

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