Formula omitted]-modules associated to the projective space of [formula omitted] matrices

Abstract

Let us consider X the complex vector space of square matrices and P ( X ) the associated projective space. Denote A the quotient algebra of all SL n ( C ) × SL n ( C ) -invariant differential operators modulo those vanishing on SL n ( C ) × SL n ( C ) -invariant functions. We show that the inverse image functor π + , where π : X \\ { 0 } → P ( X ) is the canonical projection, establishes an equivalence of categories between the category of regular holonomic D -modules on the projective space P ( X ) and the quotient category of graded A -modules of finite type modulo those supported by { 0 } . Then we deduce a combinatorial classification of regular holonomic D P ( X ) -modules. To cite this article: P. Nang, C. R. Acad. Sci. Paris, Ser. I 340 (2005).