Journal of Algebraic Combinatorics

, Volume 13, Issue 2, pp 151–172 | Cite as

On a Conjectured Formula for Quiver Varieties

  • Anders Skovsted Buch
Article

Abstract

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.

quiver varieties Littlewood-Richardson rule Schur functions Young tableaux 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Anders Skovsted Buch
    • 1
  1. 1.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA

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