The Algebraic Structure of the $gl(n|m)$ Color Calogero-Sutherland Models

Abstract

We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop algebras. Also, a super $W_{\infty }$ algebra for the SUSY CS model is constructed.

LaTeX, 13 pages

References in corpus (7)

• Yang-Baxter equation in spin chains with long range interactions
• Integrable Systems for Particles with Internal Degrees of Freedom
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• Representations of Super Yangian
• $gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra
• The Quantum Super Yangian and Casimir Operators of $U_q(gl(M|N))$
• Super-Yangian Y(gl(1|1)) and Its Oscillator Realization

Cited by in corpus (3)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$