Braid group actions of quantum Borcherds-Bozec algebras

Zhaobing Fan; Bolun Tong

paper

Braid group actions of quantum Borcherds-Bozec algebras

arXiv:2110.03367

Abstract

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