A note on q-oscillator realizations of Uq(gl(M|N)) for Baxter Q-operators

We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra Uq(gl(M|N)), and obtain q-oscillator realizations of the contracted algebras proposed in [1]. Instead of factoring out the invariant subspaces, we make reduction on generators of the q-oscillator algebra, which gives a shortcut to the problem. Based on this result, we obtain explicit q-oscillator representations of a Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)) for Baxter Q-operators.