  S.-Y. Pan decomposes the uniform projection of the Weil representation of a
finite symplectic-odd orthogonal dual pair, in terms of Deligne-Lusztig virtual
characters, assuming that the order of the finite field is large enough. In
this paper we use Pan's decomposition to study the theta correspondence for
this kind of dual pairs, following the approach of Adams-Moy and
Aubert-Michel-Rouquier. Our results give the theta correspondence between
unipotent representations and certain quadratic unipotent representations.
