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This article is cited in 28 scientific papers (total in 28 papers)
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General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$
S. E. Derkacheva, A. N. Manashovbc a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b Institute for Theoretical Physics, University of Regensburg, Regensburg, Germany
c St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
Abstract:
The problem of constructing the $\mathrm R$-matrix is considered in the case of an integrable spin chain with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$. A fairly complete study of general $\mathrm R$-matrices acting in the tensor product of two continuous series representations of $\mathrm{SL}(\mathrm n,\mathbb C)$ is presented. On this basis, $\mathrm R$-matrices are constructed that act in the tensor product of Verma modules (which are infinite-dimensional representations of the Lie algebra $\mathrm{sl}(n)$), and also $\mathrm R$-matrices acting in the tensor product of finite-dimensional representations of the Lie algebra $\mathrm{sl}(n)$.
Received: 19.11.2008
Citation:
S. E. Derkachev, A. N. Manashov, “General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$”, Algebra i Analiz, 21:4 (2009), 1–94; St. Petersburg Math. J., 21:4 (2010), 513–577
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https://www.mathnet.ru/eng/aa1145 https://www.mathnet.ru/eng/aa/v21/i4/p1
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Abstract page: | 720 | Full-text PDF : | 294 | References: | 59 | First page: | 14 |
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