Canonical induction formulae and the defect of a character

Robert Boltje
University of California, Santa Cruz

Abstract:
We explain the idea and the machinery of canonical induction formulae with
going as little into details as possible and show that a certain version
keeps track of the $l$-defect $d(\chi)$ of an irreducible character $\chi$
of a finite group $G$ by mapping $\chi$ precisely to the $d(\chi)$-th layer
in the filtration $A\subseteq l^{-1}A\subseteq l^{-2}A\ldots$, for a prime
$l$ and a certain free abelian group $A$.

Published in:
Representation theory of finite groups; Proceedings of a special
research quarter at the Ohio State University, Spring 1995, R. Solomon (ed.),
De Gruyter, Berlin 1997, 29-44.