Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Kuniba, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209783
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes / A. Kuniba // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ.

We construct 2ⁿ+1 solutions to the Yang-Baxter equation associated with the quantum affine algebras Uq(A⁽¹⁾ₙ₋₁), Uq(A⁽²⁾₂ₙ), Uq(C⁽¹⁾ₙ), and Uq(D⁽²⁾ₙ₊₁). They act on the Fock spaces of an arbitrary mixture of particles and holes in general. Our method is based on new reductions of the tetrahedron equ...