Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209783 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 equation and an embedding of the quantum affine algebras into n copies of the q-oscillator algebra, which admits an automorphism interchanging particles and holes.
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| ISSN: | 1815-0659 |