We prove that the dimension of the Specht module of a forest C is the same as the normalized volume of the matching polytope of G. We also associate to G a symmetric function s_G (analogous to the Schur sym-metric function s_λ for a partition λ) and investigate its combinatorial and representation-theoretic properties in relation to the Specht module and Schur module of G. We then use this to define notions of standard and semistandard tableaux for forests.
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