Victor Snaith (University of Southampton)
vps@maths.soton.ac.uk
Explicit Brauer Induction is about natural formula for Brauer's induction theorem, proved in 1946. In 1952 Brauer published such a formula for Artin's induction theorem. In 1986 I found the first solution to Brauer's original problem by means of group actions and topology. In 1989 Boltje found an algebraic proof of a different formula and soon after Symonds obtained a topological construction of Boltje's formula.
In Symonds' approach one obtains the existence of Boltje's formula but not the neat, computable algebraic formula itself. In this talk I will explain how to get the algebraic formula from some simple topological together with lots of important commutative diagrams. As an application - one of many - I will explain how to obtain homomorphic stable homotopy splittings of BSp. This fixes a litany of published errors (pointed out by Bill Richter a few years ago) due to Priddy-Mitchell, Brumfiel-Madsen and others.