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TMF, 2021 Volume 208, Number 2, Pages 180–195 (Mi tmf10081)

On the quantum $\mathfrak{osp}(1|2\ell)$ Toda chain

A. A. Gerasimova, D. R. Lebedevab, S. V. Oblezincd

a Laboratory of Quantum Physics and Information, Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia
b Moscow Center for Continuous Mathematical Education, Moscow, Russia
c School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
d Alikhanov Institute for Theoretical and Experimental Physics, National Research Center "Kurchatov Institute", Moscow, Russia

Abstract: The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|\,2\ell)$ is the closest superanalogue of standard Lie algebras. We demonstrate that the corresponding $\mathfrak{osp}(1|\,2\ell)$ Toda chain is an instance of the $BC_\ell$ Toda chain. The underlying reason for this relation is discussed.

Keywords: orthosymplectic Lie superalgebra, $BC$-type root system, quantum Toda chain.

Received: 26.02.2021
Revised: 26.02.2021

DOI: 10.4213/tmf10081


 English version:
Theoretical and Mathematical Physics, 2021, 208:2, 1004–1017

Bibliographic databases:
ArXiv: 2012.08902


© Steklov Math. Inst. of RAS, 2024