Quantum group symmetry in integrable spin chains with long-range interactions

Quantum integrable systems with long-range interaction have found applications in diverse topics of physics like generalized exclusion statistics, quantum electric transport phenomena in mesoscopic systems, N=4 super Yang-Mills gauge theory, infinite matrix product states related to CFT and recent experiments involving optical lattices of ultracold Rydberg atoms. In this talk, we shall discuss about some symmetries of quantum integrable systems with long-range interaction and their physical significance. More precisely, we shall discuss how root systems related to classical Lie algebras lead to the construction of such many-body systems. We shall also discuss about Yangian `quantum group\' symmetry in Haldane-Shastry like spin chains. Then we shall describe how the `motifs\', which are suitable combinations of binary digits like `0\' and `1\', determine the degeneracy patterns of the energy levels in the spectrum of such spin chain. Finally we shall discuss about some classical vertex models which exactly reproduce the spectra and partition functions of Haldane-Shastry like spin chains.