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 $T^*(GL(N))$ to the Lie algebra $\frak{gl}_N$. The construction is based on the Gelfand-Zetlin maximal commuting subalgebra in $U(\frak{gl}_N)$. We discuss the connection with the other known integrable systems based on $T^*GL(N)$. 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.