Generalized Askey-Wilson and q-Onsager algebras: a quantum algebraic approach to multivariate orthogonal polynomials.

The central objects of this proposal are the Askey-Wilson and q-Onsager algebra. These q-deformed algebras arise as symmetry algebras of superintegrable quantum systems. We will study two generalizations, which appear when extending the systems to multiple particles, and which are algebraically derived from quantum symmetric pairs. Moreover, this allows to extend known connections with orthogonal polynomials to several variables.