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Hej Mikhail, to my knowledge, the only symmetry of the coupling constants that one can conclude (from the hermiticity of the Hamiltonian) is g_{m n \nu} ( k , q ) = g_{n m \nu}^{*} ( k + q, -q). I shadowly remember that I have read some further remarks on time-reversal-symmetry in one of Felicianos ...

Hej experts, first I want to thank you for all the effort and all the material that you are willing to share. Be assured, that your efforts are highly appreciated within the community. You are heros! I want to determine Electron-Phonon-Matrix-elements, as they are written down in Felicianos Article ...