where α ∈ {1, • • • , N -1}, which is fully delocalized among all N exciton states. Other choices are possible (see Eq. 8 in Ref. 92 for the Schur-Weyl basis). The polariton states for the HTC model are outlined in Fig. . In the absence of exciton-phonon couplings, the N -1 dark states are energetically degenerate and have the same energies as the excitation energy of the bare molecule plus the reorganization energy, as shown in Fig. . The upper and lower polaritons in resonance are also energetically separated from the dark states by an amount √ N g c when the system is in resonance (ω c = ω a + λ). However, when there is lightmatter detuning (i.e., ω c ̸ = ω a + λ), the dark states are no longer separated in energy from the upper and lower polaritons by the same amount. In particular, with negative light-matter detuning (ω c < ω a + λ), the dark states are closer in energy to the upper polariton state as illustrated in Fig. . On the other hand, with positive detuning (ω c > ω a + λ), the dark states are closer in energy to the lower polariton state as depicted in Fig. . Thus, the polariton relaxation dynamics, mediated by excitonphonon coupling in ĤSB , will be affected by the energetics of the polariton and dark states due to different energy alignments caused by the light-matter detuning.