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Relative braid group symmetries on $\imath$quantum groups of Kac-Moody type (2209.12860v3)

Published 26 Sep 2022 in math.QA and math.RT

Abstract: Recently, relative braid group actions on $\imath$quantum groups of arbitrary finite types have been constructed by Wang and the author. In this paper, we extend that construction to $\imath$quantum groups of Kac-Moody type. We formulate root vectors for $\imath$quantum groups in both recursive forms and closed $\imath$divided power forms. We show that the relative braid group symmetries send root vectors to root vectors.

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