Assuming everything is correct, and this red light is not a reflection of some other light source or something: one possible way of achieving this is that the medium is absorbing green light and emitting the red light through photoluminescence. So in this case it's technically not light changing frequency in the medium; it's "new" light produced by the medium, and it is characteristic for the particular medium. In short, if the medium absorbs green light and emits red in this process, it means that there is an allowed optical transition with energy corresponding to the green light, and then this excited state is relaxed to a lower-energy state. The latter can then relax to the ground state emitting a red photon. So technically, the spectrum of the photoluminescence contains information about the energy levels in the medium.
Note that in linear optics (single photon processes only) it can only go one-way (green to red in your example) because the energy of the green photon is higher. So the conservation of energy is not violated, and some energy is lost in the medium (e.g. on heating). This means that if you get a source of red light and shine its light on the same glass, it won't produce green light. In nonlinear optics, this is not true; for example, two photons with energies half of that of the green photon can be absorbed, and one red photon can be emitted, bit for that you need high intensity (laser light could work actually).
Of course, when I write "red" or "green" photon, I mean a photon with the energy corresponding to the wavelength of green or red light, respectively.