Geodesic
On a conjectured formula for quiver varieties
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 151-172.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In A.S. Buch and W. Fulton [ $Invent. Math$. 135 (1999), 665-687] a formula for the cohomology class of a quiver variety is proved. This formula writes the cohomology class of a quiver variety as a linear combination of products of Schur polynomials. In the same paper it is conjectured that all of the coefficients in this linear combination are non-negative, and given by a generalized Littlewood-Richardson rule, which states that the coefficients count certain sequences of tableaux called factor sequences. In this paper I prove some special cases of this conjecture. I also prove that the general conjecture follows from a stronger but simpler statement, for which substantial computer evidence has been obtained. Finally I will prove a useful criterion for recognizing factor sequences.
Keywords: quiver varieties, Littlewood-Richardson rule, Schur functions, Young tableaux 
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     author = {Buch, Anders Skovsted},
     title = {On a conjectured formula for quiver varieties},
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Buch, Anders Skovsted. On a conjectured formula for quiver varieties. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 151-172. http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a4/