Defining relations for quantum symmetric pair coideals of Kac-Moody type

Abstract

Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra $\mathfrak{g}$, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as quantum symmetric pairs, replace the fixed point Lie subalgebras by one-sided coideal subalgebras of the quantized enveloping algebra $U_q(\mathfrak{g})$. We provide a complete presentation by generators and relations for these quantum symmetric pair coideal subalgebras. These relations are of inhomogeneous $q$-Serre type and are valid without restrictions on the generalized Cartan matrix. We draw special attention to the split case, where the quantum symmetric pair coideal subalgebras are generalized $q$-Onsager algebras.

arXiv comment51 pages

References in corpus (18)

• Quantum symmetric Kac-Moody pairs
• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• Deformed Dolan-Grady relations in quantum integrable models
• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• A new (in)finite dimensional algebra for quantum integrable models
• The Universal Askey-Wilson Algebra
• Quantum symmetric spaces and related q-orthogonal polynomials
• The bar involution for quantum symmetric pairs
• Onsager symmetries in $U(1)$-invariant clock models
• The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
• Some remarks on a generalization of the superintegrable chiral Potts model
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion
• Generalized q-Onsager Algebras and Dynamical K-matrices
• A Serre presentation for the $ı$quantum groups
• Quantum spin chains from Onsager algebras and reflection $K$-matrices
• Radial part calculations for affine sl2 and the Heun KZB-heat equation