Characters of equivariant D-modules on spaces of matrices
arXiv:1507.06621 · doi:10.1112/S0010437X16007521
Abstract
We compute the characters of the simple GL-equivariant holonomic D-modules on the vector spaces of general, symmetric and skew-symmetric matrices. We realize some of these D-modules explicitly as subquotients in the pole order filtration associated to the determinant/Pfaffian of a generic matrix, and others as local cohomology modules. We give a direct proof of a conjecture of Levasseur in the case of general and skew-symmetric matrices, and provide counterexamples in the case of symmetric matrices. The character calculations are used in subsequent work with Weyman to describe the D-module composition factors of local cohomology modules with determinantal and Pfaffian support.
Reorganized the material according to the referee's suggestions. To appear in Compos. Math