Integrable Structure of Multispecies Zero Range Process
We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic R matrices of quantum affine algebra Uq(An⁽¹⁾), matrix product construction of stationary states for periodic systems, q-boson representation of Zamolo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148647 |
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| Cite this: | Integrable Structure of Multispecies Zero Range Process / A. Kuniba, M. Okado, S. Watanabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 51 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862611061632401408 |
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| author | Kuniba, A. Okado, M. Watanabe, S. |
| author_facet | Kuniba, A. Okado, M. Watanabe, S. |
| citation_txt | Integrable Structure of Multispecies Zero Range Process / A. Kuniba, M. Okado, S. Watanabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 51 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic R matrices of quantum affine algebra Uq(An⁽¹⁾), matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc. We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.
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| first_indexed | 2025-11-29T00:22:17Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148647 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T00:22:17Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kuniba, A. Okado, M. Watanabe, S. 2019-02-18T16:54:15Z 2019-02-18T16:54:15Z 2017 Integrable Structure of Multispecies Zero Range Process / A. Kuniba, M. Okado, S. Watanabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 51 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 60C9 DOI:10.3842/SIGMA.2017.044 https://nasplib.isofts.kiev.ua/handle/123456789/148647 We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic R matrices of quantum affine algebra Uq(An⁽¹⁾), matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc. We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter. This paper is a contribution to the Special Issue on Recent Advances in Quantum Integrable Systems. The
 full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2016.html.
 The authors thank Ivan Corwin, Philippe Di Francesco, Alexandr Garbali, Michio Jimbo and
 Tomohiro Sasamoto for kind interest. They also thank Jef frey Kuan for informing them of the
 interesting work [27] and Shohei Machida for letting them know the Serre relations of UA( ). Last
 but not least we thank the anonymous referees for productive suggestions to improve the paper.
 This work is supported by Grants-in-Aid for Scientific Research No. 15K04892, No. 15K13429
 and No. 16H03922 from JSPS. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Structure of Multispecies Zero Range Process Article published earlier |
| spellingShingle | Integrable Structure of Multispecies Zero Range Process Kuniba, A. Okado, M. Watanabe, S. |
| title | Integrable Structure of Multispecies Zero Range Process |
| title_full | Integrable Structure of Multispecies Zero Range Process |
| title_fullStr | Integrable Structure of Multispecies Zero Range Process |
| title_full_unstemmed | Integrable Structure of Multispecies Zero Range Process |
| title_short | Integrable Structure of Multispecies Zero Range Process |
| title_sort | integrable structure of multispecies zero range process |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148647 |
| work_keys_str_mv | AT kunibaa integrablestructureofmultispecieszerorangeprocess AT okadom integrablestructureofmultispecieszerorangeprocess AT watanabes integrablestructureofmultispecieszerorangeprocess |