  Employing the random matrix formulation of Chern-Simons theory on Seifert
manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful
in exact computations in Chern-Simons matrix models. We construct a
biorthogonal extension of the Stieltjes-Wigert polynomials, not available in
the literature, necessary to study Chern-Simons matrix models when the geometry
is a lens space. We also discuss several other results based on the properties
of the polynomials: the equivalence between the Stieltjes-Wigert matrix model
and the discrete model that appears in q-2D Yang-Mills and the relationship
with Rogers-Szego polynomials and the corresponding equivalence with an unitary
matrix model. Finally, we also give a detailed proof of a result that relates
quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert
ensemble.
