A formula for non-equioriented quiver orbits of type A A

We prove a positive combinatorial formula for the equivariant class of an orbit closure in the space of representations of an arbitrary quiver of type AA. Our formula expresses this class as a sum of products of Schubert polynomials indexed by a generalization of the minimal lace diagrams of Knutson...

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Bibliographic Details
Published in:Journal of algebraic geometry 2007-07, Vol.16 (3), p.531-546
Main Authors: Buch, Anders Skovsted, Rimányi, Richárd
Format: Article
Language:English
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Research article
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Summary:We prove a positive combinatorial formula for the equivariant class of an orbit closure in the space of representations of an arbitrary quiver of type AA. Our formula expresses this class as a sum of products of Schubert polynomials indexed by a generalization of the minimal lace diagrams of Knutson, Miller, and Shimozono. The proof is based on the interpolation method of Fehér and Rimányi. We also conjecture a more general formula for the equivariant Grothendieck class of an orbit closure.
ISSN:1056-3911
1534-7486
DOI:10.1090/S1056-3911-07-00441-9