Characters of Equivariant D-modules on Veronese Cones
summary
Veronese cone (affine image of v ↦ v^d) has local cohomology supported only in the codimension degree and for n>2 fails to be a set theoretic complete intersection, so arithmetic rank exceeds codimension. The nonzero local cohomology module is a simple GL(W)-equivariant D-module whose character is computed by decomposing the injective D0 via stabilized plethysms p_r(V) as r → ∞. Computation uses a spectral sequence tracking multiplicities and representation stability to count which irreducibles survive.
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