Title: Equivariant mirror symmetry for the weighted projective line,
Abstract: In this paper, we establish equivariant mirror symmetry for the weighted
projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong,
where the projective line was considered [{\it Geometry \& Topology}
24:2049-2092, 2017]. More precisely, we prove the equivalence of the
$R$-matrices for A-model and B-model at large radius limit, and establish
isomorphism for $R$-matrices for general radius. We further demonstrate that
the graph sum of higher genus cases are the same for both models, hence
establish equivariant mirror symmetry for the weighted projective line.