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

作者：Tsuboi Zengo^*

来源：Nuclear Physics B, 2014, 886: 1-30.

DOI：10.1016/j.nuclphysb.2014.06.017

We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U-q((g) over capl(M vertical bar N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U-q(gl(M vertical bar 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 U-q((g) over capl(M vertical bar 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 U-q((s) over capl(2 vertical bar 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].

• 出版日期2014-9