Autumn 2001, MWF 10:30-11:20
Herman Weyl established the representation theory of the orthogonal groups over fields of characteristic zero using an attractive blend of algebra and analysis. The theory is one of the enduring achievements of twentieth century mathematics. In this course, we will establish the trace character and dimension formulas of Weyl for finite dimensional continuous representations of the groups. Particularly, we will see how the trace character theory enables one to determine the mulitiplicites of the irreducible factors of a tensor product of representations. The theory and computations will be of interest to students of differential geometry and algebraic geometry as well as students of algebra.
Text: The Classical Groups by Hermann Weyl, Princeton University Press