  The classification of irreducible, spherical characters of the
infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by
finding all possible limits of normalized, irreducible characters of the
corresponding finite-dimensional groups, as the rank tends to infinity. We
solve a q-deformed version of the latter problem for orthogonal and symplectic
groups, extending previously known results for the unitary group. The proof is
based on novel determinantal and double-contour integral formulas for the
q-specialized characters.
