One well-known division of Indo-European languages is Centum - Satem. However, my wikipedia-induced understanding is that due to the existence of Tocharian it is at best unclear whether it corresponds to an actual evolution of PIE into two dialects/languages.
But perhaps I'm wrong and many serious linguists do consider the Centum - Satem division as corresponding to dialects of PIE? For example on the (striking but maybe naive?) basis of the similarity of the word "five" in Balto-Slavic, Indo-Iranian and Tocharian languages?
Are there any other binary divisions of Indo-European languages which are considered by serious linguists to correspond to an evolution of PIE into two branches? I'm particularly interested whether anyone serious considers Balto-Slavic and Indo-Iranian to have had evolved together for a while, perhaps together with other families, but in separation from Centum languages.