Woit on Geometric Representation Theory

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!

One thought on “Woit on Geometric Representation Theory

  1. 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.

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