We also give an interpretation of these invariants as an obstruction to self-symmetry under magnification, and a qualitative description of generic projection patterns. I hope to give an elementary description of this programme in my talk, which will be aimed at a general mathematical audience. Explicit bounds were given by Frobenius and Schur, but these were far from optimal. He studied linear groups over algebraically closed fields of arbitrary characteristic, for which the subgroup A must be replaced by a larger subgroup, and his methods use the classification of finite simple groups. We consider polynomial functors from vector spaces to vector spaces.
Examples are symmetric and exterior powers.
We do this by comparing the representation theory of the general linear groups and symmetric groups and using Green correspondence in the latter context. I'll give an overview of the main conjectures, the connections between them and their context. It will be a survey talk describing growth series and looking at ways to calculate them. I will also discuss a connection with the Euler characteristic and mention problems and conjectures. The talk may be of interest to computer scientists.