Quantum doubles of Fock type and bosonization

TL;DR

This paper develops a framework for bosonic and fermionic realizations of modified Reflection Equation algebras using Quantum Doubles of Fock type, linked to various symmetries from quantum groups, with applications to current braidings.

Contribution

It introduces Quantum Doubles of Fock type associated with different symmetries and demonstrates their use in bosonization and fermionization of Reflection Equation algebras.

Findings

Constructed analogs of creation and annihilation operators for involutive and Hecke symmetries.

Realized Reflection Equation algebras via Quantum Doubles of Fock type.

Applied the scheme to current braidings from Hecke symmetries using Baxterization.

Abstract

We introduce analogs of creation and annihilation operators, related to involutive and Hecke symmetries R, and perform bosonic and fermionic realization of the modified Reflection Equation algebras in terms of the so-called Quantum Doubles of Fock type. Also, we introduce Quantum Doubles of Fock type, associated with Birman-Murakami-Wenzl symmetries coming from orthogonal or simplectic Quantum Groups and exhibit the algebras obtained by means of the corresponding bosonization (fermionization). Besides, we apply this scheme to current braidings arising from Hecke symmetries R via the Baxterization procedure.