Symmetry of $osp(m|n)$ spin Calogero-Sutherland models
We introduce osp(m|n) spin Calogero-Sutherland models and find that the models have the symmetry of osp(m|n) half-loop algebra or Yangian of osp(m|n) if and only if the coupling constant of the model equals to 2/(m-n-4).
Authors: Kazuyuki Oshima
Symmetry of osp ( m | n ) spin Calogero-Sutherla nd mo dels Kazuyuki Oshima Aic hi Institute of T ec hnology 1247 Y ac higusa, Y akusa Cho, T oy ota City , Aic hi Pr efecture 470-03 92, Ja pa n e-mail : oshima@aitech.ac.jp Abstract W e in tro duce osp ( m | n ) spin C alogero-Sutherland mo dels and fin d that the m o dels hav e the s y m metry of os p ( m | n ) half-lo op algebra or Y angian of osp ( m | n ) if and only if the co upling constan t of the mo del equals to 2 m − n − 4 . Mathematics Sub ject Classifications ( 2000): 70H06, 81R12, 17B70 . Keywor ds : spin Calogero-Sutherland mo d el, Lie sup eralgebra 1 In tro duc tion The Calogero - Sutherland mo dels are one-dimensional many particle systems with long range in teractions. W e denote b y L a nd λ the num b er of pa r t icles and the coupling constan t which determines t he strength of the inte raction, resp ectiv ely . The Hamiltonian of the mo del is expressed as H = − L X j =1 ∂ 2 ∂ x 2 j + 2 λ X j
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