“The “Pittsburgh School,” of course, has its basis in Sellars, who was at Pittsburgh for the latter part of his career. McDowell and Brandom both take up a particular reading of Sellars, putting a particularly strong emphasis on what Sellars calls “the space of reasons,” and putting less of an emphasis on Sellars’ aim to unify our conception of ourselves as situated in the space of reasons with the “scientific image” of ourselves. Neither Brandom nor McDowell take up the scienctistic strain in Sellars’ thinking, making both of them, to use a phrase coined by Rorty, “Left Sellarsians.” Right Sellarsians, like Paul Churchland and Ruth Millikan, emphasize the scientistic aspect more.
McDowell and Brandom both have several (often overlapping) influences other than. McDowell’s biggest influence (bigger than Sellars) is Wittgenstein. He considers himself a Wittgensnteinian. Another big influence on McDowell was his colleague at Oxford, Gareth Evans. Brandom, while also influenced by Wittgestein (on a particular reading of him, which McDowell criticizes), is especially influenced by Rorty, his dissertation adviser. His project in semantics is very influenced by Michael Dummett, and, at least in philosophical methodology, it is also easy to see how he is influenced by his other dissertation adviser, David Lewis.
As far as German idealism goes, both McDowell and Brandom aim to usher into analytic philosophy a resurgence of some key ideas of the the German idealist movement. McDowell’s Mind and World drew heavily from (a particular reading of) Kant, and Brandom sees his project as an “attempt to bring analytic philosophy into its Hegelian phase.” Kant scholars like Stephen Engstrom and Matthew Boyle have readings of Kant that have been very influenced by McDowell, and a Pittsburgh-influenced reading of Hegel in the work of Terry Pinkard and Robert Pippin has been very influenced by Brandom.
I am a bit biased, as I’m a graduate student at one of the schools that is in the same “camp” of philosophical orientation. The school is relatively unique, but it is not limited to Pittsburgh anymore, as there are several universities with younger generation of Pittsburgh-style philosophers. Chicago has a few students of McDowell on their faculty (David Finkelstein, Mathew Boyle), as well as Jim Conant, who was a colleague of Brandom and McDowell at Pittsburgh for a while. Georgetown has also taken up a strand of Pittsburgh philosophy, with Mark Lance (a student of Brandom) and Rebecca Kukla (a student of John Haugeland) doing some very interesting work in Brandom-style pragmatics. Leipzig University is another interesting branch of Pittsburgh-style philosophy, with Sebastian Roedl, who worked with Brandom in Pittsburgh and engages in very interesting ways with his work.”