Hook restriction coefficients

Finding a combinatorial interpretation of the multiplicities of each irreducible representation of the symmetric group Sₙ in the restriction of an irreducible polynomial representation of the general linear group GLₙ(C) remains an interesting open problem in algebraic combinatorics. In this paper we interpret the multiplicities of all irreducible representations of Sₙ in the restriction of an irreducible polynomial representation of GLₙ(C) indexed by a hook partition.