Braid group actions of quantum Borcherds-Bozec algebras

2021/10/07 by Fan, Zhaobing, Tong, Bolun
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2110.03367

Abstract

In this paper, we construct the Lusztig symmetries for quantum Borcherds-Bozec algebra U_q(\mathscr g) and its weight module M∈ \mathcal O, on which the generators with real indices of U_q(\mathscr g) act nilpotently. We show that these symmetries satisfy the defining relations of the braid group, associated to the Weyl group W of U_q(\mathscr g), which gives a braid group action.

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