The ^sl(2)+^sl(2)/^sl(2) Coset Theory as a Hamiltonian Reduction of ^D(2|1;\alpha)

We show that the coset ^sl(2)+^sl(2)/^sl(2) is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra ^D(2|1;\alpha) and that the corresponding W algebra is the commutant of the U_{q}D(2|1;\alpha) quantum group.