The Chern character for classical matrix groups

Jay A. Wood

Department of Mathematics, Computer Science & Statistics, Purdue University
Calumet, Hammond, Indiana 46323-2094 

Proc. Amer. Math. Soc. 126 (1998), 1237-1244.

Abstract. We give explicit formulas for representations of classical matrix 
groups whose Chern characters have lowest order terms equal to standard 
characteristic classes. For $SO(2r)$, the Euler class $e$ does not arise in 
this way, but $2^{r-1}e$ does arise in this way.