Linear Modules Of Type-A₂ And Cluster Algebras

In this paper,we study a connection between cluster algebras and a class of linear modules of the quantum affine algebra Uqg of type A₂.By introducing a L-system of equations satisfied by the q-characters of linear modules of type A₂.We show that the equations in the L-system of type A₂ correspond to mutations in some cluster algebra（?）.every linear modules in the L-system of type A₂ correspond to some cluster variables in（?）.We also list the mutation sequences for these linear modules of type A₂.