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Abstract We construct a family of PBWD (Poincaré-Birkhoff-Witt-Drinfeld) bases for the positive subalgebras of quantum loop algebras of type $$B_{n}$$ and $$G_{2}$$, as well as their Lusztig and RTT (for type $$B_{n}$$ only) integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these $${\mathbb {Q}}(v)$$-algebras (proved earlier in [26] by completely different tools) and generalize the latter to the above $${{\mathbb {Z}}}[v,v^{-1}]$$-forms. The rational counterparts provide shuffle algebra realizations of positive subalgebras of type $$B_{n}$$ and $$G_{2}$$ Yangians and their Drinfeld-Gavarini duals. All of this generalizes the type $$A_{n}$$ results of [30].more » « less
