Factorisation of quasi K-matrices for quantum symmetric pairs
Factorisation of quasi K-matrices for quantum symmetric pairs
复制标题
量子对称对的拟 K 矩阵因式分解
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Kolb
中科院分区：
文献类型：
--
作者：
Liam Dobson;S. Kolb
The theory of quantum symmetric pairs provides a universal K-matrix which is an analog of the universal R-matrix for quantum groups. The main ingredient in the construction of the universal K-matrix is a quasi K-matrix which has so far only been constructed recursively. In this paper we restrict to the cases where the underlying Lie algebra is slndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathfrak {sl}_n$$end{document} or the Satake diagram has no black dots. In these cases we give an explicit formula for the quasi K-matrix as a product of quasi K-matrices for Satake diagrams of rank one. This factorisation depends on the restricted Weyl group of the underlying symmetric Lie algebra in the same way as the factorisation of the quasi R-matrix depends on the Weyl group of the Lie algebra. We conjecture that our formula holds in general.
The theory of quantum symmetric pairs provides a universal K-matrix which is an analog of the universal R-matrix for quantum groups. The main ingredient in the construction of the universal K-matrix is a quasi K-matrix which has so far only been constructed recursively. In this paper we restrict to the cases where the underlying Lie algebra is slndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathfrak {sl}_n$$end{document} or the Satake diagram has no black dots. In these cases we give an explicit formula for the quasi K-matrix as a product of quasi K-matrices for Satake diagrams of rank one. This factorisation depends on the restricted Weyl group of the underlying symmetric Lie algebra in the same way as the factorisation of the quasi R-matrix depends on the Weyl group of the Lie algebra. We conjecture that our formula holds in general.
DOI：
10.1515/crelle-2016-0012
发表时间：
2015-07
期刊：
Journal für die reine und angewandte Mathematik (Crelles Journal)
影响因子：
--
作者：
M. Balagovic;S. Kolb
通讯作者：
M. Balagovic;S. Kolb
DOI：
10.1090/ert/469
发表时间：
2015
期刊：
Representation Theory of the American Mathematical Society
影响因子：
--
作者：
Balagovic M
通讯作者：
Balagovic M