The positive part of has a presentation with two generators A, B that satisfy the cubic q-Serre relations. We introduce a PBW basis for , said to be alternating. Each element of this PBW basis commutes with exactly one of A, B, qAB − q−1BA. This gives three types of PBW basis elements; the elements of each type mutually commute. We interpret the alternating PBW basis in terms of a q-shuffle algebra associated with affine . We show how the alternating PBW basis is related to the PBW basis for found by Damiani in 1993.
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2019
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