2016/12/04 by Andrey Smirnov, Smirnov, Andrey
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1612.01048
openalex publication_date 2016/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we analyze the fundamental solution of the quantum difference equation (qde) for the moduli space of instantons on two-dimensional projective space. The qde is a K-theoretic generalization of the quantum differential equation in quantum cohomology. As in the quantum cohomology case, the fundamental solution of qde provides the capping operator in K-theory (the rubber part of the capped vertex). We study the dependence of the capping operator on the equivariant parameters ai of the torus acting on the instanton moduli space by changing the framing. We prove that the capping operator factorizes at ai→ 0. The rationality of the K-theoretic 1-leg capped descendent vertex follows from factorization of the capping operator as a simple corollary.