John Baez has just put out a new issue of his This Week’s Finds in Mathematical Physics, dealing partly in more detail with the material about Clifford modules mentioned here a couple weeks ago. I’ve added as the first comment here something he had some trouble submitting as a comment to the older posting on this topic.
John briefly mentions a relation of all this to Bott periodicity in topology, using a very abstract homotopy construction involving spectra. A more concrete version of this can be found in Milnor’s book on Morse theory. For the relation of Clifford algebras and K-theory, the standard refererence is the 1964 paper “Clifford Modules” by Atiyah, Bott and Shapiro published in the journal “Topology”. The crucial fact they describe is how the Thom isomorphism in K-theory (which is essentially the same fact as Bott periodicity) is related to the structure of Clifford modules. Greg Landweber has recently worked out an interesting equivariant version of this story.
Greg also has a nice new paper with Megumi Harada about the K-theory of a symplectic quotient, that looks like it should imminently appear on the arXiv.
John also mentions some recent work of Dror Bar-Natan, Thang Le and Dylan Thurston on the Duflo isomorphism. This is a beautiful story, and also has a relation to Clifford algebras that John doesn’t mention. For this, see Eckhard Meinrenken’s talk at the 2002 ICM in Beijing.