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The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
Інший ID:
2010 Mathematics Subject Classification: 37K10; 81Q80; 05E05
DOI:10.3842/SIGMA.2014.006
DOI:10.3842/SIGMA.2014.006
Посилання:
The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy / A. Zabrodin // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 42 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
The author thanks A. Alexandrov, A. Gorsky, V. Kazakov, S. Khoroshkin, I. Krichever, S. Leurent,
M. Olshanetsky, A. Orlov, T. Takebe, Z. Tsuboi, and A. Zotov for discussions. Referees’
remarks which helped to improve the manuscript are gratefully acknowledged. This work was
supported in part by RFBR grant 11-02-01220, by joint RFBR grants 12-02-91052-CNRS, 12-
02-92108-JSPS and by Ministry of Science and Education of Russian Federation under contract
8207 and by grant NSh-3349.2012.2 for support of leading scientific schools.
Дата:
2014
Переглядів:
672
Завантажень:
297
Анотація:
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
