The Yangian Deformation of the W-Algebras and and the Calogero-Sutherland model

Denis Bernard (1) , Kazuhiro Hikami , Miki Wadati

1 SPhT - Service de Physique Théorique

The Yangian symmetry Y(su($n$)) of the Calogero-Sutherland-Moser spin model is reconsidered. The Yangian generators are constructed from two non-commuting su($n$)-loop algebras. The latters generate an infinite dimensional symmetry algebra which is a deformation of the $W_\infty$-algebra. We show that this deformed $W_\infty$-algebra contains an infinite number of Yangian subalgebras with different deformation parameters.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Denis Bernard, Kazuhiro Hikami, Miki Wadati. The Yangian Deformation of the W-Algebras and and the Calogero-Sutherland model. Developments of Integrable Sys- tems and Long-Ranged Interaction Models, 1995, Nankai, China. ⟨hal-03086707⟩