*Article* **Symmetry of Dressed Photon**

**Hiroyuki Ochiai**

Institute of Mathematics for Industry, Kyushu University, Fukuoka 819-0395, Japan; ochiai@imi.kyushu-u.ac.jp

**Abstract:** Motivated by describing the symmetry of a theoretical model of dressed photons, we introduce several spaces with Lie group actions and the morphisms between them depending on three integer parameters *n* ≥ *r* ≥ *s* on dimensions. We discuss the symmetry on these spaces using classical invariant theory, orbit decomposition of prehomogeneous vector spaces, and compact reductive homogeneous space such as Grassmann manifold and flag variety. Finally, we go back to the original dressed photon with *n* = 4,*r* = 2,*s* = 1.

**Keywords:** dressed photon; Grassmann manifold; flag manifold; pre-homogeneous vector space; invariants
