The sℓ̂(2)⊕sℓ̂(2)/sℓ̂(2) coset theory as a Hamiltonian reduction of D̂(2|1;α)

We show that the coset sℓ̂(2)k1⊕sℓ̂(2)k2/sℓ̂(2)k1+k2 is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra D̂(2|1;α) and that the corresponding W algebra is the commutant of the UqD(2|1;α) quantum group.