Quantum doubles of Fock type and bosonization
Quantum Algebra
2022-12-27 v1
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.
Cite
@article{arxiv.2212.12699,
title = {Quantum doubles of Fock type and bosonization},
author = {Dimitry Gurevich and Pavel Saponov},
journal= {arXiv preprint arXiv:2212.12699},
year = {2022}
}