Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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


Authors: Anders Skovsted Buch and Richárd Rimányi
Journal: J. Algebraic Geom. 16 (2007), 531-546
DOI: https://doi.org/10.1090/S1056-3911-07-00441-9
Published electronically: February 21, 2007
MathSciNet review: 2306279
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Abstract | References | Additional Information

Abstract: 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 $ A$. 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.


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Anders Skovsted Buch
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
Email: asbuch@math.rutgers.edu

Richárd Rimányi
Affiliation: Department of Mathematics, The University of North Carolina at Chapel Hill, CB #3250, Phillips Hall, Chapel Hill, New Carolina 27599
Email: rimanyi@email.unc.edu

DOI: https://doi.org/10.1090/S1056-3911-07-00441-9
Received by editor(s): October 10, 2005
Published electronically: February 21, 2007
Additional Notes: We thank the referee for several helpful suggestions to our exposition.

American Mathematical Society