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This article is cited in 7 scientific papers (total in 7 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.
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
Linking options:
https://www.mathnet.ru/eng/tmf307https://doi.org/10.4213/tmf307 https://www.mathnet.ru/eng/tmf/v130/i3/p355
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Abstract page: | 586 | Full-text PDF : | 241 | References: | 63 | First page: | 1 |
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