Title: A third look at weight diagrams
Speaker: Professor Nikolai Vavilov
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:
In the talk I describe a completely elementary approach to calculations in exceptional Chevalley groups which is based on the weight diagrams (alias, crystal graphs) of their minimal modules. Imagine you pretend to calculate inside G=E6, E7 or E8 on a beach and have forgotten your Bourbaki at home. I'm going to tell you a purely combinatorial way to reconstruct the structure constants, the action constants, action of the extended Weyl group, equations for the orbit of the highest weight vector, etc. from the weight diagram alone. I'll speak about some applications to the structure theory and K-theory of exceptional groups and sketch the key step of the ``decomposition of unipotents'' for E6 and E7.Date: Tuesday, October 17, 2000