A note on quantum products of Schubert classes in a Grassmannian

2006/08/22 by Anderson, Dave
#05E10 #14M15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608546

Abstract

Given two Schubert classes σ_λ and σ_μ in the quantum cohomology of a Grassmannian, we construct a partition ν, depending on λ and μ, such that σ_ν appears with coefficient 1 in the lowest (or highest) degree part of the quantum product σ_λ⋆σ_μ. To do this, we show that for any two partitions λ and μ, contained in a k-by-(n-k) rectangle and such that the 180-degree rotation of one does not overlap the other, there is a third partition ν, also contained in the rectangle, such that the Littlewood-Richardson number c_λμ^ν is 1.

Related

• Quantum multiplication of Schur polynomials
• Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C
• Quantum cohomology of Grassmannians
• On the quantum product of Schubert classes
• Quantum Grassmannians and their Associated Quantum Schubert Varieties at roots of unity