What makes this interesting is that, until now, Republic has only flown flights on behalf of other, larger airlines under codeshare agreements. Hence why you can't actually (for now anyway!) buy a ticket on Republic Airlines. You may have flown on Republic but the regional aircraft you flew on was marketed and sold by one of the many carriers Republic operates flights on behalf of including US Airways, Delta, United, American and Continental.
This will be Republic's first foray into selling, marketing, revenue managing etc their own flights - today all of these functions are handled by the larger major carriers.
The bigger question is how the major carriers who now provide the majority of Republic's business through contract flying will feel about suddenly competing against a supplier - particularly at a time when the regional airline industry has an excess supply or regional jets. It is hard to see how United could be happy about competing with Frontier in Denver at the same time Republic (which now owns Frontier) is providing flights for hire for United!
We doubt Delta, AA, Continental or US Airways are relishing similar situations either- they were probably hoping for Midwest and Frontier to be removed as competitors rather than bolstered.
On the other hand, the Street loved it - RJET was up 46% today