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Dirac operators for compact coadjoint orbits (and for matrix algebras that converge to them?)

QMAP Seminar

Speaker: Marc Rieffel, UC Berkeley
Location: 2112 MSB
Start time: Thu, Apr 2 2009, 3:10PM

Physicists say that sequences of matrix algebras converge to the 2-sphere or other coadjoint orbits of compact Lie groups. They then go on to use "vector bundles" for the matrix algebras that they say correspond to vector bundles on the coadjoint orbits, Dirac operators for the matrix algebras that correspond to Dirac operators on the coadjoint orbits, Yang-Mills, etc. I will indicate briefly why physicists want to do this, and how I make sense of the convergence of matrix algebras to coadjoint orbits. In order to try to understand the situation for Dirac operators, I have recently studied Dirac operators on coadjoint orbits, emphasizing a global approach so as to facilitate comparison with possible Dirac operators for matrix algebras. I will report on what I have found.