Faithful action of braid group on bosonic extensions

TL;DR

This paper proves that the braid group action on the bosonic extension of quantum groups is faithful, extending the understanding of symmetries in quantum algebra.

Contribution

It establishes the faithfulness of the braid group action on bosonic extensions, a significant step in quantum group symmetry theory.

Findings

Braid group action on bosonic extensions is faithful

Generalizes Lusztig's symmetries on quantum groups

Provides foundational results for quantum algebra symmetries

Abstract

The braid group action on the bosonic extension of the quantum group has been introduced in recent works, and it can be regarded as a generalization of Lusztig's symmetries on the quantum group. In this notes, we prove the faithfulness of this braid group action.