  We give a new proof of the computation of Hodge integrals we have previously
obtained for the quantum singularity (FJRW) theory of chain polynomials. It
uses the classical localization formula of Atiyah--Bott and we phrase our proof
in a general framework that is suitable for future studies of gauged linear
sigma models (GLSM). As a by-product, we obtain the first equivariant version
of mirror symmetry without concavity, generalizing the work of
Chiodo--Iritani--Ruan on the Landau--Ginzburg side.
