Equivariant D-modules on 2x2x2 hypermatrices

Abstract

Let V be the space of 2x2x2 complex hypermatrices, endowed with the natural group action of GL=GL(2,C)^3. The category of GL-equivariant coherent D-modules on V is equivalent to the category of representations of a quiver with relations. In this article, we give a construction of each simple object and study their GL-equivariant structure. Using this information, we go on to explicitly describe the corresponding quiver with relations. As an application, we compute all iterations of local cohomology with support in the orbit closures of V.

16 pages. v4: corrected relations of the quiver, added characteristic cycles, added Lemma 3.13

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• Local cohomology with support in generic determinantal ideals
• Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians
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Cited by in corpus (2)

• Equivariant D-modules on alternating senary 3-tensors
• On categories of equivariant D-modules