Аннотация:
We start from known solutions of the Yang–Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group SL(2,C) or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional representation in one or both spaces. In this way we obtain very simple explicit formulas embracing rational and trigonometric finite-dimensional solutions of the Yang–Baxter equation. Finally, we construct these finite-dimensional solutions by means of the fusion procedure and find a nice agreement between two approaches.
Ключевые слова:
Yang–Baxter equation; principal series; modular double; fusion.
Образец цитирования:
Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov, “From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation”, SIGMA, 12 (2016), 028, 34 pp.
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\paper From Principal Series to Finite-Dimensional Solutions of the Yang--Baxter Equation
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1110
https://www.mathnet.ru/rus/sigma/v12/p28
Эта публикация цитируется в следующих 8 статьяx:
Yury A. Neretin, “On Derkachov–Manashov R-matrices for the principal series of unitary representations”, Journal of Mathematical Physics, 65:5 (2024)
П. В. Антоненко, П. А. Валиневич, “Cтатистические веса и процедура слияния для рациональной семивершинной SOS модели”, Вопросы квантовой теории поля и статистической физики. 29, Зап. научн. сем. ПОМИ, 520, ПОМИ, СПб., 2023, 17–49
I. C. H. Ip, “On tensor product decomposition of positive representations of Uq˜q(sl(2,R))”, Lett. Math. Phys., 111:2 (2021), 39
С. Э. Деркачёв, В. П. Спиридонов, “О 6j-символах для группы SL(2,C)”, ТМФ, 198:1 (2019), 32–53; S. È. Derkachev, V. P. Spiridonov, “The 6j-symbols for the SL(2,C) group”, Theoret. and Math. Phys., 198:1 (2019), 29–47
П. А. Валиневич, П. В. Антоненко, “Универсальная R-матрица для рациональной семивершинной модели”, Вопросы квантовой теории поля и статистической физики. 26, Зап. научн. сем. ПОМИ, 487, ПОМИ, СПб., 2019, 100–105
R. Frassek, “The non-compact xxz spin chain as stochastic particle process”, J. Phys. A-Math. Theor., 52:33 (2019), 335202
D. Chicherin, V. P. Spiridonov, “The hyperbolic modular double and the Yang-Baxter equation”, Representation Theory, Special Functions and Painleve Equations - RIMS 2015, Advanced Studies in Pure Mathematics, 76, eds. H. Konno, H. Sakai, J. Shiraishi, T. Suzuki, Y. Yamada, Math Soc Japan, 2018, 95–123
Bosnjak G., Mangazeev V.V., “Construction of R -matrices for symmetric tensor representations related to Uq(^sln)”, J. Phys. A-Math. Theor., 49:49 (2016), 495204
Цитирование в формате AMSBIB
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