Double and triple Givental's \(J\)-functions for stable quotients invariants (Q2256296)

The J-functions were introduced by A. Givental, based on the analysis of the symplectic geometry of the cohomological field theories. These functions contain the data, enough to reconstruct all correlators of a cohomological field theory. In this paper the author considers the moduli spaces of the stable quotients and certain correlators (called SQ invariants) on it. It is shown that in the certain cases these correlators are all rational numbers. Packing the SQ invariants into the certain generating function the author defines an analogue of the Givental's J-function. Later comparing it to the J-function of the Gromov-Witten theory author gets a mirror symmetry type result.