Equivariant Chow classes of matrix orbit closures

Abstract

Let $G$ be the product $G{L}_r(C)\times (C^{\times }{)}^n$. We show that the $G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$ matrices is determined by a matroid. To do this, we split the natural surjective map from the $G$ equvariant Chow ring of the space of matrices to the torus equivariant Chow ring of the Grassmannian. The splitting takes the class of a Schubert variety to the corresponding factorial Schur polynomial, and also has the property that the class of a subvariety of the Grassmannian is mapped to the class of the closure of those matrices whose row span is in the variety.

11 pages. Theorem 3.5 here proves a version of the main result of arXiv:1306.1810v5, the proof of which contained an error

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