Asymptotic Representations of Quantum Affine Superalgebras

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

Fundamental representations of quantum affine superalgebras and R-matrices

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.Comment: 28 pages, to appear in Transformation Group

Theta series for quantum loop algebras and Yangians

We introduce and study a family of power series, which we call Theta series, whose coefficients are in the tensor square of a quantum loop algebra. They arise from a coproduct factorization of the T-series of Frenkel--Hernandez, which are leading terms of transfer matrices of certain infinite-dimensional irreducible modules over the upper Borel subalgebra in the category O of Hernandez--Jimbo. We prove that each weight component of a Theta series is polynomial. As applications, we establish a decomposition formula and a polynomiality result for R-matrices between an irreducible module and a finite-dimensional irreducible module in category O. We extend T-series and Theta series to Yangians by solving difference equations determined by the truncation series of Gerasimov--Kharchev--Lebedev--Oblezin. We prove polynomiality of Theta series by interpreting them as associators for triple tensor product modules over shifted Yangians.Comment: 65 pages, comments welcom

Disability types and children’s schooling in Africa

The Sustainable Development Goals (SDGs) set up by the United Nations include an overarching principle of “leaving no one behind” and aim for, among other goals, equal access to education for children with disabilities. Our study contributes to the knowledge on the school enrolment of disabled children with different disability types, with a focus here on eight countries in Sub-Saharan Africa. Comparing the situation with children without disabilities as a benchmark, we assess early school enrolment for young children below ten years old, school enrolment for older children aged 10–17 years old, and the dropout rates of children from school. We perform our analysis as a natural experiment where different types of disabilities are considered as random treatments, which allows us to assume that the average deviation in certain school performance indicators from the average for non-disabled children is a result of the disability type, specifically vision, hearing, walking, intellectual capacity, and multi-disability. Our study finds that, compared with non-disabled children, children with vision and hearing disabilities do not lag behind in school enrolment. In contrast, children with walking disability have a higher risk of starting school late. Children with intellectual disabilities are less likely to enrol in school, less likely to remain enrolled, and more likely to drop out than their counterfactual peers. Children with multiple disabilities tend to experience the most severe challenges in enrolling at school, both at a young age and later. However, once enrolled in school, children with multiple disabilities are not more likely to drop out earlier than other children. Based on the first and probably the only large-scale application to date of the standard Washington Group Child function module as a disability measurement tool, our study is the first comprehensive multi-country study of disabled children’s schooling in Sub-Saharan Africa based on recent nationally representative data