Universal K-matrices for quantum Kac-Moody algebras
| Autor: | Appel, Andrea, Vlaar, Bart |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Represent. Theory 26 (2022), 764-824 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/ert/623 |
| Popis: | 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 Balagovi\'c 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 $U_qL\mathfrak{sl}_2$. Comment: Minor edits. 57 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|