Alternating signs of quiver coefficients
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- by Anders Skovsted Buch;
- J. Amer. Math. Soc. 18 (2005), 217-237
- DOI: https://doi.org/10.1090/S0894-0347-04-00473-4
- Published electronically: November 18, 2004
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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.References
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Bibliographic Information
- Anders Skovsted Buch
- Affiliation: Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark
- MR Author ID: 607314
- Email: abuch@imf.au.dk
- 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: https://doi.org/10.1090/S0894-0347-04-00473-4
- MathSciNet review: 2114821