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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Alternating signs of quiver coefficients
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by Anders Skovsted Buch PDF
J. Amer. Math. Soc. 18 (2005), 217-237 Request permission


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
  • MR Author ID: 607314
  • Email:
  • Received by editor(s): January 5, 2004
  • Published electronically: November 18, 2004
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 18 (2005), 217-237
  • MSC (2000): Primary 05E15; Secondary 14M15, 14M12, 19E08
  • DOI:
  • MathSciNet review: 2114821