Young diagrams also parametrize the irreducible polynomial representations of the general linear group (when they have at most nonempty rows), or the irreducible representations of the special linear group (when they have at most nonempty rows), or the irreducible complex representations of the special unitary group (again when they have at most nonempty rows). In these cases semistandard tableaux with entries up to play a central role, rather than standard tableaux; in particular it is the number of those tableaux that determines the dimension of the representation.
