**4. Discussion**

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We describe the symmetry of equations of dressed photon in a general manner. The tensor *S* is understood as an affine version of Plücker coordinates of Grassmann manifold Grass(4, 2, <sup>R</sup>). The splitting expression of the tensor *T*ˆ is related with an affine version of flag manifold Flag(4; 1, 2, <sup>R</sup>). We find the off-shell condition (8) chooses the special fiber of the homogeneous bundle. This mathematical interpretation of the choice may have a physical interpretation, especially in the context of Clebsch variables, however, which must be a future work. We also remark that the existence of the symmetry in arbitrary dimension suggests a feedback from the theory of dressed photon to the theory of reductive dual pairs on the pullback of nilpotent orbits [6], which is also a topic of future study.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This research was partially supported by 2019 IMI Joint Use Research Program Workshop "Basic mathematical studies on dressed photon phenomena". The author thanks the anonymous reviewer for their questions and comments, which helped them to improve the quality of this article.

**Conflicts of Interest:** The author declares no conflict of interest.
