On the Singular Rank of a Representation

Abstract

Consider the reductive dual pair $({\text {S}}{{\text {p}}_{2n}},{{\text {O}}_{p,q}})$. We prove that if $\pi$ is a representation of ${\text {S}}{{\text {p}}_{2n}}$ coming from duality correspondence with some representation of ${{\text {O}}_{p,q}}$ then the wave front set of $\pi$ has rank $\leq p + q$. For $p + q < n$ this implies a result stated (but not proved) by Howe.

Locations

• Proceedings of the American Mathematical Society - View