2018/06/06 by András C. Lőrincz, Uli Walther, Lőrincz, András C. +1 · 2 citations
Mathematics · #14F10 #14M27 #16G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1806.02428
openalex publication_date 2018/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 isomorphic 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).