On a class of integrable systems connected with GL(N,\RR)

Abstract

In this paper we define a new class of the quantum integrable systems associated with the quantization of the cotangent bundle $T^{\ast }(GL(N))$ to the Lie algebra ${\mathfrak{gl}}_N$. The construction is based on the Gelfand-Zetlin maximal commuting subalgebra in $U({\mathfrak{gl}}_N)$. We discuss the connection with the other known integrable systems based on $T^{\ast }GL(N)$. The construction of the spectral tower associated with the proposed integrable theory is given. This spectral tower appears as a generalization of the standard spectral curve for integrable system.

LaTeX, 13 pages