Specialization maps for shuffle algebras of type $B_n$ and $G_2$

We define a filtration of Feigin-Odesskii’s shuffle algebras of type B_n and G_2 using specialization maps, generalizing the results in type A_n case given by Negut and Tsymbaliuk. These filtrations are compatible with a class of PBW type bases for the quantum current algebras of type B_n and G_2.