Alternating signs of quiver coefficients

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 KK-theoretic quiver coefficients have alternating signs and gives an explicit combinatorial formula for these coef...

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2005-01, Vol.18 (1), p.217-237
Main Author: Buch, Anders Skovsted
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Discrete mathematics
Integers
Line segments
Mathematical functions
Mathematical permutation
Mathematics
Polynomials
Research article
Tableaux
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Summary: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 KK-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.
ISSN:0894-0347
1088-6834
DOI:10.1090/S0894-0347-04-00473-4