K-theoretic J-functions of type A flag varieties

2011/10/14 by Kaisa Taipale, Taipale, Kaisa · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1110.3117

23 pages; comments welcome

arxiv created 2011/10/14 · arxiv updated 2011/10/17

Abstract

The J-function in Gromov-Witten theory is a generating function for one-point genus zero Gromov-Witten invariants with descendants. Here we give formulas for the quantum K-theoretic J-functions of type A flag manifolds and conjectural formulas for other types. Some K-theoretic tools for computation are also provided. As an application, we prove the quantum K-theoretic J-function version of the abelian-nonabelian correspondence for Grassmannians and products of projective space.

Cited by

• Lifting I-functions from the Grassmannians to their cotangent bundles
• Towards small quantum Chern character

Related

• Quantum K-theory of flag varieties via non-abelian localization
• Gromov-Witten Invariants for Abelian and Nonabelian Quotients
• Quantum K-theory of projective spaces and confluence of q-difference\n equations
• Quantum cohomology of flag varieties
• Quantum K-theory of Grassmannians