2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93464The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the $A_N$ and $B_N$ type models and explain the degeneracy structure of the later. We identify the commuting constants of motion and the generators of a linear $W_\infty$ algebra associated with the $B_N$ system.8 pages, REVTeX, Completely revised, few new equations and references are addedQuantum PhysicsCondensed MatterHigh Energy Physics - Theorytext