On the classification of regular holonomic D-modules on skew-symmetric matrices

We give a classification of regular holonomic D-modules on 2m×2m-skew-symmetric matrices related to the action of the general linear group GL(2m,C). Actually we establish one more case of the conjecture by T. Levasseur (Levasseur, 2009 [12, p. 508, Conjecture 5.17]).