Braid symmetries on bosonic extensions

TL;DR

This paper introduces braid symmetries on bosonic extensions, showing they satisfy braid relations and preserve key bases, leading to new subalgebras and insights into tensor product decompositions.

Contribution

It presents a novel family of automorphisms satisfying braid relations on bosonic extensions, with implications for basis preservation and algebraic structure.

Findings

Automorphisms satisfy braid relations

Preservation of global and crystal bases

Construction of subalgebras with PBW basis

Abstract

We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal basis. Using this braid group action, we define a subalgebra for each positive braid word, which possesses the PBW type basis. As an application, we show that the tensor product decomposition of the positive bosonic extionsion,