## 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.

Original language | English (US) |
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Pages (from-to) | 151-172 |

Number of pages | 22 |

Journal | Journal of Algebraic Combinatorics |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics

## Keywords

- Littlewood-Richardson rule
- Quiver varieties
- Schur functions
- Young tableaux