Because the Thermostat is hardwired into the Furnace you can do this without any logic involved. You need to install a Relay connected to GH on the stat and when GH goes high your relay trips and will then trigger the HEPA filter. If you want the HEPA to turn ON if the fan is running (low, med, or High) then you would require 3 Relays wired in an OR sequence (GL, GM, GH on the tstat).

We do this all the time with boiler pumps. Saves on programming time and is not linked to programming which could fail.

If you need to do this programmatically it would be quite ease
If Fan is Running = High
Turn ON HEPA (Close relay I am assuming)
Else
Turn Off HEPA (Open Relay)

Again Programmatically this is possible, but to do this using simple relay's will be much easier and is a fail safe solution.