On a Conjectured Formula for Quiver Varieties

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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 languageEnglish (US)
Pages (from-to)151-172
Number of pages22
JournalJournal of Algebraic Combinatorics
Volume13
Issue number2
DOIs
StatePublished - Mar 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Keywords

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

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