  Let Sp_V(F) be the group of isometries of a symplectic vector space V over a
finite field F of odd cardinality. The group Sp_V(F) possesses distinguished
representations--- the Weil representations. We know that they are compatible
with base change in the sense of Shintani for a finite extension F'/F. The
result is also true for the group of similitudes of V.
