A General Theory of Canonical Induction Formulae

Robert Boltje
University of California, Santa Cruz
http://math.uscs.edu/~boltje

Abstract:
So far there exist three independent constructions of two
different canonical versions of Brauer's induction theorem for
complex characters due to V. Snaith, P. Symonds, and the author.
`Canonical' in this context means functorial with respect to
restrictions along group homomorphisms.
In this article we axiomatize the situation in which the above
canonical induction formulae are constructed. Mackey functors
and related structures arise in this way naturally as a
convenient language. This approach allows to construct canonical
induction formulae for arbitrary Mackey functor. In particular
we obtain canonical induction formulae for the Brauer character
ring, the group of projective characters, the ring of trivial
source modules, and the ring of linear source modules. In most
cases, it is not difficult to construct such formulae over the
rational numbers. A much more subtle que