The Lie algebraic structure of extended Sutherland models

Abstract

We disclose the Lie algebraic structure of two extended Sutherland models. Their Hamiltonians are BC_N, and A_N Sutherland Hamiltonians with some additional terms. We show that both Hamiltonians can be written in the quadratic forms of generators of the Lie algebra gl(N+1).

9 pages, added note and reference, corrected typos