Filtration of tensor product of local Weyl modules for sl₍+₁t

In this paper, we consider the tensor product of local Weyl modules for sl₍+₁t whose highest weights are multiples of the first and n^th fundamental weights. We determine the graded character of these tensor product modules in terms of the graded character of local Weyl modules and prove that these modules admit a filtration whose successive quotients are either truncated Weyl modules or fusion products of Demazure modules. Furthermore, we establish that the truncated Weyl modules appearing as quotients in the filtration of tensor products of local Weyl modules of sl₃t are indeed isomorphic to fusion products of irreducible sl₃t-modules which establish the independence of a family of fusion product modules of sl₃t from the set of its evaluation parameters.