Quantum cohomology of Grassmannians

Abstract

We give elementary proofs of the main theorems about (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, Siebert and Tian's presentation, and a recent theorem of Fulton and Woodward about the minimal q-power which appears in a product of two Schubert classes.

8 pages

References in corpus (1)

• Degree of the generalized Plücker embedding of a Quot scheme and Quantum cohomology

Cited by in corpus (11)

• Quantum Pieri rules for isotropic Grassmannians
• Quantum sheaf cohomology on Grassmannians
• Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers
• On the quantum product of Schubert classes
• Transformation formulas in Quantum Cohomology
• Direct proof of the quantum Monk's formula
• Quantum cohomology of symplectic flag manifolds
• Quantum Pieri rules for tautological subbundles
• Positivity of minuscule quantum K-theory
• Gromov-Witten invariants and rational curves on Grassmannians
• Quantum cohomology of partial flag manifolds