Matching polytopes and Specht modules

Liu, Ricky

doi:10.1090/S0002-9947-2011-05516-9

Matching polytopes and Specht modules
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by Ricky Ini Liu

Trans. Amer. Math. Soc. 364 (2012), 1089-1107

DOI: https://doi.org/10.1090/S0002-9947-2011-05516-9

Published electronically: October 4, 2011

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Abstract:

We prove that the dimension of the Specht module of a forest $G$ 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 symmetric function $s_\lambda$ for a partition $\lambda$) 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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