Defining relations of quantum symmetric pair coideal subalgebras

Abstract

Abstract We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantised enveloping algebras of Kac–Moody type. Our methods are based on star products on noncommutative ${\mathbb N}$ -graded algebras. The resulting defining relations are expressed in terms of continuous q-Hermite polynomials and a new family of deformed Chebyshev polynomials.