Fundamental representations of quantum affine superalgebras and R-matrices

Abstract

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices between two fundamental representations are computed; a cyclicity (and so simplicity) condition on tensor products of fundamental representations is proved.

28 pages, to appear in Transformation Groups

References in corpus (1)

• Local Weyl modules and cyclicity of tensor products for Yangians

Cited by in corpus (6)

• Asymptotic Representations of Quantum Affine Superalgebras
• Baxter operators and asymptotic representations
• Length-two representations of quantum affine superalgebras and Baxter operators
• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• A functor for constructing $R$-matrices in the category $\mathcal{O}$ of Borel quantum loop algebras
• Quasi-solvable lattice models for ${\mathrm{Sp}}_{2n}$ and ${\mathrm{SO}}_{2n+1}$ Demazure atoms and characters