Gröbner–Shirshov Bases for Irreducible sln + 1-Modules

We determine the Gröbner–Shirshov bases for finite-dimensional irreducible representations of the special linear Lie algebra sln + 1 and construct explicit monomial bases for these representations. We also show that each of these monomial bases is in 1–1 correspondence with the set of semistandard Young tableaux of a given shape.