Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators

We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(gl̂(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of _{U q}(g l(M|N)) in the FRT formulation and obtain explicit solutions of the graded Yang-Baxter equation in terms of q-oscillator superalgebras. These solutions correspond to L-operators for Baxter Q-operators. We also discuss an extension of these representations to the ones for contracted algebras of Uq(gl̂(M|N)) by considering the action of renormalized generators of the other side of the Borel subalgebra. We define model independent universal Q-operators as the supertrace of the universal R-matrix and write universal T-operators in terms of these Q-operators based on shift operators on the supercharacters. These include our previous work on Uq(sl̂(2|1)) case [1] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T- and Q-functions in [2,3].