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TMF, 2007, Volume 150, Number 3, Pages 371–390 (Mi tmf5985)  

This article is cited in 6 scientific papers (total in 6 papers)

Transition function for the Toda chain

A. V. Silant'evab

a Joint Institute for Nuclear Research
b Département de Mathématiques, Université d'Angers

Abstract: We use the method of $\Lambda$-operators developed by Derkachov, Korchemsky, and Manashov to derive eigenfunctions for the open Toda chain. Using the diagram technique developed for these $\Lambda$-operators, we reproduce the Sklyanin measure and study the properties of the $\Lambda$-operators. This approach to the open Toda chain eigenfunctions reproduces the Gauss–Givental representation for these eigenfunctions.

Keywords: Toda chain, separation of variables, $Q$-operators

DOI: https://doi.org/10.4213/tmf5985

Full text: PDF file (690 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 150:3, 315–331

Bibliographic databases:

Received: 13.03.2006
Revised: 08.07.2006

Citation: A. V. Silant'ev, “Transition function for the Toda chain”, TMF, 150:3 (2007), 371–390; Theoret. and Math. Phys., 150:3 (2007), 315–331

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kozlowski K.K., “Aspects of the Inverse Problem for the Toda Chain”, J. Math. Phys., 54:12 (2013), 121902  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Derkachov S.E. Manashov A.N., “Iterative Construction of Eigenfunctions of the Monodromy Matrix For Sl(2, C) Magnet”, J. Phys. A-Math. Theor., 47:30 (2014), 305204  crossref  mathscinet  zmath  isi  scopus
    3. Kozlowski K.K., “Unitarity of the Sov Transform For the Toda Chain”, Commun. Math. Phys., 334:1 (2015), 223–273  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Derkachov S.E. Manashov A.N. Valinevich P.A., “Gustafson Integrals For Sl(2, C) Spin Magnet”, J. Phys. A-Math. Theor., 50:29 (2017), 294007  crossref  mathscinet  zmath  isi  scopus
    5. Derkachov S.E. Manashov A.N., “Spin Chains and Gustafson'S Integrals”, J. Phys. A-Math. Theor., 50:29 (2017), 294006  crossref  mathscinet  zmath  isi  scopus
    6. S. E. Derkachov, P. A. Valinevich, “Separation of variables for the quantum $SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin $B$-operator”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 110–146  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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