This article is cited in 1 paper

Bethe Manifolds Associated with Classical Root Systems

V. V. Meshcheryakov

Kolomna State Pedagogical Institute

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.

UDC: 517.986.9

Received: 23.03.2007

DOI: 10.4213/mzm4084

 English version: Mathematical Notes, 2007, 82:5, 635–642

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