On a Conjectured Formula for Quiver Varieties
- Anders Skovsted Buch
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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.
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- On a Conjectured Formula for Quiver Varieties
Journal of Algebraic Combinatorics
Volume 13, Issue 2 , pp 151-172
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- quiver varieties
- Littlewood-Richardson rule
- Schur functions
- Young tableaux
- Author Affiliations
- 1. Mathematics Department, Massachusetts Institute of Technology, Building 2, Room 275, Cambridge, MA, 02139, USA