Asymptotic Representations of Quantum Affine Superalgebras

Abstract

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called $q$-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.

References in corpus (8)

• Baxter's Q-operators for supersymmetric spin chains
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• Local Weyl modules and cyclicity of tensor products for Yangians
• Affinization of category O for quantum groups
• Fundamental representations of quantum affine superalgebras and R-matrices
• Baxter operators and asymptotic representations
• Length-two representations of quantum affine superalgebras and Baxter operators
• Q-operator and fusion relations for $C_q^{(2)}(2)$

Cited by in corpus (8)

• RTT realization of quantum affine superalgebras and tensor products
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Length-two representations of quantum affine superalgebras and Baxter operators
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Universal R-matrix of quantum affine gl(1,1)
• Elliptic quantum groups and Baxter relations
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system