Defining relations of quantum symmetric pair coideal subalgebras

TL;DR

This paper explicitly determines the defining relations of quantum symmetric pair coideal subalgebras in quantized Kac-Moody algebras using star products, q-Hermite, and deformed Chebyshev polynomials.

Contribution

It provides a complete set of defining relations for these subalgebras, introducing new polynomial families and methods for their explicit description.

Findings

Derived explicit relations for all quantum symmetric pair coideal subalgebras.

Connected the relations to continuous q-Hermite and deformed Chebyshev polynomials.

Established a new approach using star products on noncommutative graded algebras.

Abstract

We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantized 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.