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We establish PBW type bases for quantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for quantum groups of each rank 1 type. We show that our PBW type bases give rise to integral bases for the modified quantum groups. The leading terms of our bases can be identified with the usual PBW bases in the theory of quantum groups.
Lu et al. (Wed,) studied this question.