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

Abstract

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 also discuss an extension of these representations to the ones for contracted algebras of U_q(gl(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 U_q(sl(2|1)^) case [arXiv:0805.4274] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T-and Q-functions in [arXiv:0906.2039, arXiv:1109.5524].

37 pages; v2: misprints corrected, details added; v3: presentation improved

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Cited by in corpus (14)

• Matrix product formula for Macdonald polynomials
• Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
• RTT realization of quantum affine superalgebras and tensor products
• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators
• The universal R-matrix and factorization of the L-operators related to the Baxter Q-operators
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• Asymptotic Representations of Quantum Affine Superalgebras
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Length-two representations of quantum affine superalgebras and Baxter operators
• Orthosymplectic superoscillator Lax matrices
• Drinfeld basis for string-inspired Baxter operators
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Integrable systems and AdS/CFT duality
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system