Transformation Groups

, Volume 22, Issue 3, pp 631–643

EQUIVARIANT CHOW CLASSES OF MATRIX ORBIT CLOSURES

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Abstract

Let G be the product GLr(C) × (C×)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.

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsWestern Washington UniversityBellinghamUSA
  2. 2.School of Mathematical SciencesQueen Mary University of LondonLondonUnited Kingdom

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