Corpus ID: 119120893

Canonical bases arising from quantum symmetric pairs of Kac-Moody type

@article{Bao2018CanonicalBA,
  title={Canonical bases arising from quantum symmetric pairs of Kac-Moody type},
  author={Huanchen Bao and W. Wang},
  journal={arXiv: Quantum Algebra},
  year={2018}
}
For quantum symmetric pairs $(\mathbf{U}, \textbf{U}^\imath)$ of Kac-Moody type, we construct $\imath$canonical bases for the highest weight integrable $\mathbf{U}$-modules and their tensor products regarded as $\mathbf{U}^\imath$-modules, as well as an $\imath$canonical basis for the modified form of the $\imath$quantum group $\mathbf{U}^\imath$. A key new ingredient is a family of explicit elements called $\imath$divided powers, which are shown to generate the integral form of $\dot{\bf{U… Expand
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