Universal K-matrices for quantum Kac-Moody algebras

Andrea Appel*, Bart Vlaar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra H endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection equation, yielding an action of cylindrical braid groups on tensor products of its representations. We prove that new examples of such universal K-matrices arise from quantum symmetric pairs of Kac-Moody type and depend upon the choice of a pair of generalized Satake diagrams. In finite type, this yields a refinement of a result obtained by Balagović and Kolb, producing a family of non-equivalent solutions interpolating between the quasi-K-matrix originally due to Bao and Wang and the full universal K-matrix. Finally, we prove that this construction yields formal solutions of the generalized reflection equation with a spectral parameter in the case of finite-dimensional representations over the quantum affine algebra UqLsl2.

Original languageEnglish
Pages (from-to)764-824
Number of pages61
JournalRepresentation Theory
Volume26
DOIs
Publication statusPublished - 19 Jul 2022

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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