Specialization maps for shuffle algebras of type $B_{n}$ and $G_{2}$

TL;DR

This paper introduces a filtration method for shuffle algebras of types B_n and G_2 using specialization maps, extending previous type A_n results, and aligns these filtrations with PBW bases for related quantum current algebras.

Contribution

It generalizes the construction of specialization-based filtrations from type A_n to types B_n and G_2, connecting them with PBW bases.

Findings

Established filtrations compatible with PBW bases for types B_n and G_2

Extended the specialization map approach to new algebra types

Provided a framework for analyzing shuffle algebras beyond type A_n

Abstract

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.