Wednesdays 12:40–2pm, 939 Evans, CCN 54506
We will explore Gukov and Witten's proposal of brane quantization as a new and improved geometric quantization, following their construction of the irreducible unitary representations of SL(2,R). Their proposal offers possible new insight to the solution of a classical unsolved problem, a geometric construction of the unitary nontempered representations of a real semisimple Lie group. This will be an excuse for us to review the basics of the structure and representation theory of real semisimple Lie groups, where many of the statements are beautiful, yet sophisticated refinements of analogues for compact Lie groups. Familiarity with the representation theory of the latter is strongly desirable, although the first 67 lectures should be accessible just from knowledge of SU(2) and the basics of hyperKaehler manifolds.
References will be updated.
Time and energy permitting, we will review the application of the same new brany ideas to ChernSimons theory. (This seems unlikely now)
Date 
Topic 
Speaker 
References 
1/28 
Introduction and outline of the seminar 
Teleman 
8, 9 
2/4 
Branes and GukovWitten quantization 1 
Ryan 
1, 2 Notes 
2/11 
Branes and GukovWitten quantization 2 
Ryan 
1, 2 
2/18 
HyperKähler structures on coadjoint orbits  Teleman 
10 
2/25 
Representations of SL(2, R)
via brane quantization 
Alex Takeda 
1, 2. Notes 
2/27  Review of Representation theory of compact Lie groups  Ben Gammage  
3/4  Representations of SL(2, R) via brane quantization 2  Alex Takeda  
3/6 
Structure of real semisimple Lie groups  QC 
3, 4 
3/11 
HarishChandra module, infinitesimal characters, admissible representations  Kiran Luecke 
3 
3/18 
Discrete series representations. Character formula.  Teleman 
3, 4, 5 
3/25 
Spring Break  
4/1 
Parabolic induction and Langlands classification  George Melvin 
3, 4, 6 
4/8 
Geometry and Physics lectures  no meeting  see announcement  
4/15  ??? 


4/22  ??? 

4/29  Coadjoint orbits and their geometric quantization  Teleman 
(Berkeley Library and sometimes source links)