  In the present paper few steps are undertaken towards the description of the
qubit-qutrit pair - quantum bipartite system composed of two and three level
subsystems. The computational difficulties with the construction of the local
unitary polynomial invariants are discussed. Calculations of the Molien
functions and Poincare series for the qubit-qubit and qubit-qutrit local
unitary invariants are outlined and compared with the known results. The
requirement of positive semi-definiteness of the density operator is formulated
explicitly as a set of inequalities in five Casimir invariants of the algebra
su(6).
