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Integrable Structure of Multispecies Zero Range Process
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Integrable Structure of Multispecies Zero Range Process
Інший ID:
2010 Mathematics Subject Classification: 81R50; 60C9
DOI:10.3842/SIGMA.2017.044
DOI:10.3842/SIGMA.2017.044
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
516
Завантажень:
244
Анотація:
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.
