A novel kind of a multicomponent hierarchy of discrete soliton equations and its application

Based on a Lie algebra $\hat g$, we presented a method for constructing multicomponent integrable hierarchies of discrete soliton equations. As an application of the method, we consider the modified Toda spectral problem and obtain a new multicomponent integrable hierarchy of lattice equations with two arbitrary constants, which can be reduced to two multicomponent integrable systems, one of which is the famous Toda lattice system.