  Persymmetric Jacobi matrices are invariant under reflection with respect to
the anti-diagonal. The associated orthogonal polynomials have distinctive
properties that are discussed. They are found in particular to be also
orthogonal on the restrictions either to the odd or to the even points of the
complete orthogonality lattice. This is exploited to design very efficient
inverse problem algorithms for the reconstruction of persymmetric Jacobi
matrices from spectral points. Isospectral deformations of such matrices are
also considered. Expressions for the associated polynomials and their weights
are obtained in terms of the undeformed entities.
