Corpus ID: 119141350

A Serre presentation for the $\imath$quantum groups

@article{Chen2018ASP,
  title={A Serre presentation for the \$\imath\$quantum groups},
  author={X. Chen and M. Lu and W. Wang},
  journal={arXiv: Representation Theory},
  year={2018}
}
Let $(\bf U, \bf U^\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node. We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations. The verification of new $\imath$Serre relations is reduced to some new q-binomial identities. Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters. 
8 Citations

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