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Zap. Nauchn. Sem. POMI, 2006, Volume 335, Pages 134–163 (Mi znsl213)  

This article is cited in 13 scientific papers (total in 13 papers)

Factorization of the $\mathrm{R}$-matrix. I

S. È. Derkachev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We study the general rational solution of the Yang–Baxter equation with the symmetry algebra $s\ell(3)$. The $R$-operator acting in the tensor product of two arbitrary representations of the symmetry algebra can be represented as the product of the simpler “building blocks” – $\mathbb R$-operators. The $\mathbb R$-operators are constructed explicitly and have simple structure. We construct in a such way the general rational solution of the Yang–Baxter equation with the symmetry algebra $s\ell(3)$. To illustrate the factorization in the simplest situation we treat also the $s\ell(2)$ case.

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English version:
Journal of Mathematical Sciences (New York), 2007, 143:1, 2773–2790

Bibliographic databases:

UDC: 517.9
Received: 14.05.2006

Citation: S. È. Derkachev, “Factorization of the $\mathrm{R}$-matrix. I”, Questions of quantum field theory and statistical physics. Part 19, Zap. Nauchn. Sem. POMI, 335, POMI, St. Petersburg, 2006, 134–163; J. Math. Sci. (N. Y.), 143:1 (2007), 2773–2790

Citation in format AMSBIB
\by S.~\`E.~Derkachev
\paper Factorization of the $\mathrm{R}$-matrix.~I
\inbook Questions of quantum field theory and statistical physics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 335
\pages 134--163
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 1
\pages 2773--2790

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    This publication is cited in the following articles:
    1. Sergey É Derkachov, Alexander N. Manashov, “$\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain”, SIGMA, 2 (2006), 084, 20 pp.  mathnet  crossref  mathscinet  zmath
    2. J. Math. Sci. (N. Y.), 151:2 (2008), 2880–2893  mathnet  crossref  mathscinet
    3. Derkachov S., Karakhanyan D., Kirschner R., “Yang–Baxter $\mathscr R$-operators and parameter permutations”, Nuclear Phys. B, 785:3 (2007), 263–285  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Belitsky A.V., Derkachov S.E., Korchemsky G.P., Manashov A.N., “The Baxter $Q$-operator for the graded $\mathrm{SL}(2|1)$ spin chain”, J. Stat. Mech. Theory Exp., 2007, no. 1, P01005, 63 pp.  crossref  mathscinet  isi  elib  scopus
    5. S. E. Derkachev, A. N. Manashov, “General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$”, St. Petersburg Math. J., 21:4 (2010), 513–577  mathnet  crossref  mathscinet  zmath  isi
    6. Derkachov S.E., Manashov A.N., “Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains”, Journal of Physics A-Mathematical and Theoretical, 42:7 (2009), 075204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Bazhanov V.V., Lukowski T., Meneghelli C., Staudacher M., “A Shortcut to the Q-Operator”, J. Stat. Mech.-Theory Exp., 2010, P11002  crossref  isi  elib  scopus
    8. S. È. Derkachev, V. P. Spiridonov, “Yang–Baxter equation, parameter permutations, and the elliptic beta integral”, Russian Math. Surveys, 68:6 (2013), 1027–1072  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. S. È. Derkachev, V. P. Spiridonov, “Finite-dimensional representations of the elliptic modular double”, Theoret. and Math. Phys., 183:2 (2015), 597–618  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. S. E. Derkachov, D. I. Chicherin, “Matrix factorization for solutions of the Yang–Baxter equation”, J. Math. Sci. (N. Y.), 213:5 (2016), 723–742  mathnet  crossref  mathscinet
    11. Fuksa J., Kirschner R., “Correlators with s?2 Yangian symmetry”, Nucl. Phys. B, 914 (2017), 1–42  crossref  mathscinet  zmath  isi  elib  scopus
    12. Kamil Yu. Magadov, Vyacheslav P. Spiridonov, “Matrix Bailey Lemma and the Star-Triangle Relation”, SIGMA, 14 (2018), 121, 13 pp.  mathnet  crossref
    13. N. M. Belousov, S. E. Derkachev, “$Q$-operator dlya kvantovoi modeli NSh”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 34–65  mathnet
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