The generators of the classical Specht module satisfy intricate relations. Weintroduce the Specht matroid, which keeps track of these relations, and theSpecht polytope, which also keeps track of convexity relations. We establishbasic facts about the Specht polytope, for example, that the symmetric groupacts transitively on its vertices and irreducibly on its ambient real vectorspace. A similar construction builds a matroid and polytope for a tensorproduct of Specht modules, giving "Kronecker matroids" and "Kroneckerpolytopes" instead of the usual Kronecker coefficients. We dub this process ofupgrading numbers to matroids and polytopes "matroidification," giving two moreexamples. In the course of describing these objects, we also give an elementaryaccount of the construction of Specht modules different from the standard one.Finally, we provide code to compute with Specht matroids and their Chow rings.
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