Alternating signs of quiver coefficients

Buch, Anders¹

¹ Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark

Journal of the American Mathematical Society, Tome 18 (2005) no. 1, pp. 217-237

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-04-00473-4

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