The Weyl groupoid and its action on the affine super-Yangian

V. D. Volkov ; V. A. Stukopin

Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 30, Tome 532 (2024), pp. 119-135

Résumé

We define the action of the Weyl groupoid on the affine super-Yangian $Y_{\hbar}(\widehat{sl}(m|n, \Pi))$ of the special linear Kac-Moody superalgebra $\hat{sl}(m|n, \Pi) $, given by an arbitrary system of simple roots $\Pi$. Affine super-Yangians of this type form a category. Morphisms in this category are given by the action of the elements of the Weyl groupoid. All super-Yangians from this category are isomorphic as associative superalgebras, but morphisms defined by the action of elements of a Weyl groupoid do not preserve coproducts. We describe coproducts on super-Yangians and their relation to the Weyl groupoid action.