Just wanted to point out to everyone that Peter Woit, of the blog *Not Even Wrong* is doing a great job blogging on the relations between representation theory of Lie groups, functions on Lie groups and differential operators. And he promises there will be physics before the end!

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Thanks for the advertisement David!

For the mathematically sophisticated, what I’m aiming for is to explain a recent set of ideas about representation theory (due to people like Kostant, Vogan, Alekseev-Meinrenken, Huang-Pandzic, and others) that goes under the name “Dirac cohomology”. What’s known as the “non-commutative Weil algebra” is also part of the story. The connection to physics is basically that I argue that these are the right ideas for dealing with gauge symmetries in quantum theory, related to what physicists know as “BRST symmetry”.

There’s a lot of beautiful, but not widely-known mathematics that goes into this story, so my idea was to start by blogging about this, working my way up to explaining the Dirac cohomology/BRST business, and possible applications. Even if they’re not interested in the direction I’m going with this, I hope that some people will find the expository pieces useful. The next few postings will be about the Clifford algebra of a Lie algebra, then the non-commutative Weil algebra, then Dirac cohomology.