Simple sln+1sln+1-module structures on U(h)U(h)

We study the category MM consisting of U(sln+1)U(sln+1)-modules whose restriction to U(h)U(h) is free of rank 1, in particular we classify isomorphism classes of objects in MM and determine their submodule structure. This leads to new sln+1sln+1-modules. For n=1n=1 we also find the central characters and derive an explicit formula for taking tensor product with a simple finite dimensional module.