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TMF, 2002, Volume 130, Number 3, Pages 355–382 (Mi tmf307)  

This article is cited in 5 scientific papers (total in 5 papers)

Unitary Representations of the Quantum Lorentz Group and Quantum Relativistic Toda Chain

M. A. Olshanetskya, V.-B. K. Rogovb

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Moscow State University of Railway Communications

Abstract: We give a group theory interpretation of the three types of $q$-Bessel functions. We consider a family of quantum Lorentz groups and a family of quantum Lobachevsky spaces. For three values of the parameter of the quantum Lobachevsky space, the Casimir operators correspond to the two-body relativistic open Toda-chain Hamiltonians whose eigenfunctions are the modified $q$-Bessel functions of the three types. We construct the principal series of unitary irreducible representations of the quantum Lorentz groups. Special matrix elements in the irreducible spaces given by the $q$-Macdonald functions are the wave functions of the two-body relativistic open Toda chain. We obtain integral representations for these functions.

DOI: https://doi.org/10.4213/tmf307

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English version:
Theoretical and Mathematical Physics, 2002, 130:3, 299–322

Bibliographic databases:

Received: 08.10.2001

Citation: M. A. Olshanetsky, V.-B. K. Rogov, “Unitary Representations of the Quantum Lorentz Group and Quantum Relativistic Toda Chain”, TMF, 130:3 (2002), 355–382; Theoret. and Math. Phys., 130:3 (2002), 299–322

Citation in format AMSBIB
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\paper Unitary Representations of the Quantum Lorentz Group and Quantum Relativistic Toda Chain
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\pages 355--382
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 130
\issue 3
\pages 299--322
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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. Lowe DA, “q-deformed de Sitter/conformal field theory correspondence”, Physical Review D, 70:10 (2004), 104002  crossref  mathscinet  adsnasa  isi
    2. Olshantesky MA, Rogov VBK, “Poisson kernel on the quantum Lobachevsky spaces”, Acta Applicandae Mathematicae, 81:1 (2004), 269–274  crossref  mathscinet  isi  scopus
    3. M. A. Olshanetsky, V.-B. K. Rogov, “dS–AdS Structures in Noncommutative Minkowski Spaces”, Theoret. and Math. Phys., 144:3 (2005), 1315–1343  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Simon Ruijsenaars, “A Relativistic Conical Function and its Whittaker Limits”, SIGMA, 7 (2011), 101, 54 pp.  mathnet  crossref
    5. Hallnaes M., Ruijsenaars S., “Kernel Functions and Backlund Transformations for Relativistic Calogero–Moser and Toda Systems”, J. Math. Phys., 53:12 (2012), 123512  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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