  From the q-oscillator solution to the tetrahedron equation associated with a
quantized coordinate ring, we construct solutions to the Yang-Baxter equation
by applying a reduction procedure formulated earlier by S. Sergeev and the
first author. The results are identified with the quantum R matrices for the
infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2) corresponding
to an affinization of Verma modules of their subalgebras isomorphic to
U_q(sl_2) and U_{q^4}(sl_2).
