Canonical bases arising from quantum symmetric pairs

Huanchen Bao University of Maryland, College Park Weiqiang Wang University of Virginia

Quantum Algebra mathscidoc:1804.29001

Best Paper Award in 2018

We develop a general theory of canonical bases for quantum symmetric pairs (U, U^i) with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable U-modules and their tensor products regarded as U^i-modules. We also construct a canonical basis for the modified form of the i-quantum group U^i. 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.
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  • To appear in Invent. Math.
@inproceedings{huanchencanonical,
  title={Canonical bases arising from quantum symmetric pairs},
  author={Huanchen Bao, and Weiqiang Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180410024031660862035},
}
Huanchen Bao, and Weiqiang Wang. Canonical bases arising from quantum symmetric pairs. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180410024031660862035.
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