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SIGMA, 2009, Volume 5, 029, 17 pages (Mi sigma375)  

This article is cited in 3 scientific papers (total in 3 papers)

Limits of Gaudin Systems: Classical and Quantum Cases

Alexander Chervova, Gregorio Falquib, Leonid Rybnikova

a Institute for Theoretical and Experimental Physics, 25 Bolshaya Cheremushkinskaya Str., 117218 Moscow, Russia
b Dipartimento di Matematica e Applicazioni, Università di Milano - Bicocca, via R. Cozzi, 53, 20125 Milano, Italy

Abstract: We consider the XXX homogeneous Gaudin system with $N$ sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new “Gaudin” algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of “Manin matrices” to provide explicit generators of the Gaudin Algebras in the quantum case.

Keywords: Gaudin models; Hamiltonian structures; Gaudin algebras

DOI: https://doi.org/10.3842/SIGMA.2009.029

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Full text: http://emis.mi.ras.ru/.../029
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Bibliographic databases:

ArXiv: 0903.1604
Document Type: Article
MSC: 82B23; 81R12; 17B80; 81R50
Received: November 1, 2008; in final form February 25, 2009; Published online March 9, 2009
Language: English

Citation: Alexander Chervov, Gregorio Falqui, Leonid Rybnikov, “Limits of Gaudin Systems: Classical and Quantum Cases”, SIGMA, 5 (2009), 029, 17 pp.

Citation in format AMSBIB
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\by Alexander Chervov, Gregorio Falqui, Leonid Rybnikov
\paper Limits of Gaudin Systems: Classical and Quantum Cases
\jour SIGMA
\yr 2009
\vol 5
\papernumber 029
\totalpages 17
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\crossref{https://doi.org/10.3842/SIGMA.2009.029}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chervov A., Falqui G., Rubtsov V., “Algebraic properties of Manin matrices. I”, Adv. in Appl. Math., 43:3 (2009), 239–315  crossref  mathscinet  zmath  isi  scopus
    2. Musso F., “Loop coproducts, Gaudin models and Poisson coalgebras”, J. Phys. A, 43:43 (2010), 434026, 17 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Aguirre L., Felder G., Veselov A.P., “Gaudin subalgebras and stable rational curves”, Compos Math, 147:5 (2011), 1463–1478  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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