From quantum difference equation to Dubrovin connection of affine type A quiver varieties

This is the continuation of the article {Z23}. In this article we will give a detailed analysis of the quantum difference equation of the equivariant K-theory of the affine type A quiver varieties. We will give a good representation of the quantum difference operator ML(z) such that the monodromy operator Bₘ(z)in the formula can be written in the Uq(sl₂)-form or in the Uq(gl̂₁)-form. We also give the detailed analysis of the connection matrix for the quantum difference equation in the nodal limit p→0. Using these two results, we prove that the degeneration limit of the quantum difference equation is the Dubrovin connection for the quantum cohomology of the affine type A quiver varieties, and the monodromy representation for the Dubrovin connection is generated by the monodromy operators Bₘ.