  The meridian maps of the full Homfly skein of the annulus are linear
endomorphisms induced by the insertion of a meridian loop, with either
orientation, around a diagram in the annulus. The eigenvalues of the meridian
maps are known to be distinct, and are indexed by pairs of partitions of
integers p and n into k and k* parts respectively.
  We give here an explicit formula for a corresponding eigenvector as the
determinant of a (k*+k)x(k*+k) matrix whose entries are skein elements
corresponding to partitions with a single part. This extends the results of
Kawagoe and Lukac, for the case p=0, giving a basis for the subspace of the
skein spanned by closed braids all oriented in the same direction. Their
formula uses the Jacobi-Trudy determinants for Schur functions in terms of
complete symmetric functions. Our matrices have a similar pattern of entries in
k rows, and a modified pattern in k* rows, resulting in a combination of closed
braids with up to n strings oriented in one direction and p in the reverse
direction.
  We discuss the 2-variable knot invariants resulting from decoration of a knot
by these skein elements, and their relation to unitary quantum invariants.
