  Let F be a p-adic field of odd residual characteristic. Let G(n) and G`(n) be
the metaplectic double covers of the general symplectic group and the
symplectic group attached to the 2n dimensional symplectic space over F. Let T
be a genuine, possibly reducible, unramified principal series representation of
G(n). In these notes we give an explicit formulas for a spanning set for the
space of Spherical Whittaker functions attached to T. For odd n, and
generically for even n, this spanning set is a basis. The signicant property of
this set is that each of its elements is unchanged under the action of the Weyl
group of G`(n). If n is odd then each element in the set has an equivariant
property that generalizes the uniqueness result of Gelbart, Howe and
Piatetski-Shapiro proven for G(1). Using this symmetric set, we construct a
family of reducible genuine unramified principal series representations which
have more then one generic constituent. This family contains all the reducible
genuine unramified principal series representations induced from a unitary data
and exists only for n even.
