The paper “5D partition functions, q-Virasoro systems, and integrable spin chains“, co-authored by Fabrizio Nieri, Sara Pasquetti, Filippo Passerini (Princeton & Ecole Normale Superieure), and Alessandro Torrielli has been accepted for publication in the Journal of High Energy Physics. The final-form manuscript can be found on the arXiV here. In the paper they analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. When the 5d mass parameters are analytically continued to suitable values, the S5 and S4 x S1 partition functions degenerate to those for S3 and S2 x S1. This mechanism is explained via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, they axiomatically derive a set of associated reflection coefficients, and show they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. These particular c-functions are then linked to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin chains, obtained taking different limits of the XYZ model to XXZ-type.