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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Alternating signs of quiver coefficients


Author: Anders Skovsted Buch
Journal: J. Amer. Math. Soc. 18 (2005), 217-237
MSC (2000): Primary 05E15; Secondary 14M15, 14M12, 19E08.
Published electronically: November 18, 2004
MathSciNet review: 2114821
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a formula for the Grothendieck class of a quiver variety, which generalizes the cohomological component formulas of Knutson, Miller, and Shimozono. Our formula implies that the $K$-theoretic quiver coefficients have alternating signs and gives an explicit combinatorial formula for these coefficients. We also prove some new variants of the factor sequences conjecture and a conjecture of Knutson, Miller, and Shimozono, which states that their double ratio formula agrees with the original quiver formulas of the author and Fulton. For completeness we include a short proof of the ratio formula.


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Additional Information

Anders Skovsted Buch
Affiliation: Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark
Email: abuch@imf.au.dk

DOI: http://dx.doi.org/10.1090/S0894-0347-04-00473-4
PII: S 0894-0347(04)00473-4
Keywords: Quiver variety, quiver coefficient, degeneracy locus, Grothendieck polynomial, Zelevinsky permutation, factor sequence
Received by editor(s): January 5, 2004
Published electronically: November 18, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.