  For any natural numbers n,r, we construct an algebra P_n^r via generators and
quadratic relations, and show that it deforms the W-algebra of gl_{nr} with
respect to a nilpotent with Jordan block decomposition r+...+r. We introduce a
surjective morphism from half of the quantum toroidal algebra of gl_n to P_n^r,
and show that the action of the quantum toroidal algebra on the K-theory groups
of the moduli spaces of parabolic sheaves factors through P_n^r.
