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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209783 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862629395121831936 |
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| author | Kuniba, A. |
| author_facet | Kuniba, A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T13:42:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209783 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:42:56Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kuniba, A. 2025-11-26T12:20:48Z 2018 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. 1815-0659 2010 Mathematics Subject Classification: 81R50; 17B37; 16 arXiv: 1803.01586 https://nasplib.isofts.kiev.ua/handle/123456789/209783 https://doi.org/10.3842/SIGMA.2018.067 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. The author thanks the organizers of the MATRIX Program Non-Equilibrium Systems and Special Functions at the University of Melbourne (Creswick, 8 January 2018 – 2 February 2018), where a part of this work was done. This work is supported by Grants-in-Aid for Scientific Research No. 15K13429 from JSPS. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes Article published earlier |
| spellingShingle | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes Kuniba, A. |
| title | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes |
| title_full | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes |
| title_fullStr | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes |
| title_full_unstemmed | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes |
| title_short | Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes |
| title_sort | tetrahedron equation and quantum r matrices for q-oscillator representations mixing particles and holes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209783 |
| work_keys_str_mv | AT kunibaa tetrahedronequationandquantumrmatricesforqoscillatorrepresentationsmixingparticlesandholes |