Canonical bases arising from quantum symmetric pairs

• 成果类型: Article
• 署名作者: Bao, Huanchen; Wang, Weiqiang
• 署名单位: University System of Maryland; University of Maryland College Park; University of Virginia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0801-5
• 发表日期: 2018
• 页码: 1099-1177
• 关键词: quantized enveloping-algebras; zonal spherical-functions; coideal subalgebras; tensor-products; crystal bases

摘要

We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical bases for the finite-dimensional simple -modules and their tensor products regarded as -modules. We also construct a canonical basis for the modified form of the quantum group . To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank one), and integrality of the intertwiners.