Abstract
Recently, relative braid group symmetries on \(\imath \)quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, generalizing that finite-type construction, we establish relative braid group symmetries on \(\imath \)quantum groups of locally quasi-split Kac–Moody type. We formulate root vectors for \(\imath \)quantum groups in both recursive forms and closed \(\imath \)divided power forms. The higher rank formulas of relative braid group symmetries are given by root vectors. We show that the relative braid group symmetries send root vectors to root vectors.
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Acknowledgements
The author would like to thank his advisor Weiqiang Wang for many helpful conversations and advices. The author thanks Yaolong Shen for helpful comments and suggestions. The author also thanks anonymous referees for many valuable comments. This work is partially supported by the GRA fellowship of Wang’s NSF Grant DMS-2001351.
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Zhang, W. Relative braid group symmetries on \(\imath \)quantum groups of Kac–Moody type. Sel. Math. New Ser. 29, 59 (2023). https://doi.org/10.1007/s00029-023-00861-y
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DOI: https://doi.org/10.1007/s00029-023-00861-y