RTT realization of quantum affine superalgebras and tensor products

Abstract

We use the RTT realization of the quantum affine superalgebra associated with the Lie superalgebra $\mathfrak{gl}(M,N)$ to study its finite-dimensional representations and their tensor products. In the case $\mathfrak{gl}(1,1)$, the cyclicity condition of tensor products of finite-dimensional simple modules is determined completely in terms of zeros and poles of rational functions. This in turn induces cyclicity of some particular tensor products of Kirillov-Reshetikhin modules related to $\mathfrak{gl}(M,N)$.

24 pages

References in corpus (5)

• Quantum Deformations of the One-Dimensional Hubbard Model
• Baxter's Q-operators for supersymmetric spin chains
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$
• Asymptotic Representations of Quantum Affine Superalgebras

Cited by in corpus (14)

• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
• Length-two representations of quantum affine superalgebras and Baxter operators
• PBWD bases and shuffle algebra realizations for $U_v(L{\mathfrak{sl}}_n),U_{v_1,v_2}(L{\mathfrak{sl}}_n),U_v(L\mathfrak{sl}(m|n))$ and their integral forms
• Universal R-matrix of quantum affine gl(1,1)
• Elliptic quantum groups and Baxter relations
• A functor for constructing $R$-matrices in the category $\mathcal{O}$ of Borel quantum loop algebras
• Schur-Weyl duality for quantum toroidal superalgebras
• R-Matrix presentation of quantum affine algebra in type $A_{2n-1}^{(2)}$
• Two-parameter quantum general linear supergroups
• Quantum Berezinian for quantum affine superalgebra $U_q({\widehat{gl}}_{M|N})$