  The charge density wave (CDW) in 1T-TiSe2 accompanied by the periodic lattice
distortion has a nontrivial symmetry configuration. The symmetry is important
as an indication of the mechanism and a cue for experimental probes. We examine
the symmetry of the system and clear up the connection of electronic structures
between the normal and the CDW states. Especially, we unravel the consequential
irreducible representations (IRs) of electronic states and, more ahead, those
of gap functions among bands when the CDW occurs. Normally symmetry-related
topology will be achieved directly, so we assert that the theory is valuable
and practical for the search of topological CDW insulators.
