1205.1471 (Zengo Tsuboi)

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

Zengo Tsuboi

We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(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 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 U_q(sl(2|1)^) case [arXiv:0805.4274] in part, and also give a cue for operator realization of our Wronskian-like formulas on T-and Q-functions in [arXiv:0906.2039, arXiv:1109.5524].

View original: http://arxiv.org/abs/1205.1471