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Matematicheskie Zametki, 2007, Volume 82, Issue 5, Pages 709–717
DOI: https://doi.org/10.4213/mzm4084 (Mi mzm4084) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Bethe Manifolds Associated with Classical Root Systems

V. V. Meshcheryakov

Kolomna State Pedagogical Institute
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DOI: https://doi.org/10.4213/mzm4084
Abstract: The Calogero–Sutherland model [1] describes the state of a finite number of nonrelativistic particles on the circle (or on the hyperbola) interacting by the inverse-square law. For each classical root system (of the type $A_{n-1},B_n,C_n,D_n$), we describe the Bethe manifolds related to the Calogero–Sutherland model. In each case, the dimension of the manifold is calculated and its constitutive equations are given.
Keywords: root system, Bethe manifold, Calogero–Sutherland model, nonrelativistic particle, Weyl group.
Received: 23.03.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 5, Pages 635–642
DOI: https://doi.org/10.1134/S0001434607110065
Bibliographic databases:
UDC: 517.986.9
Language: Russian
Citation: V. V. Meshcheryakov, “Bethe Manifolds Associated with Classical Root Systems”, Mat. Zametki, 82:5 (2007), 709–717; Math. Notes, 82:5 (2007), 635–642
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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