MSI Colloquium

4pm Thursday 16 October 2003

Karin Erdmann
University of Oxford

Some fractals in the representation theory of symmetric and general linear groups

We are interested in representations of symmetric groups S_r, general linear groups GL_n(K) (for K an infinite field of prime characteristic p) and related algebras. In both cases the irreducible representations, or decomposition numbers, over characteristic p, are not known; and to find them is a major open problem. Using Schur algebras and tools from representation theory of algebras, we explain why finding decomposition numbers for symmetric groups is the same problem as finding decomposition numbers for general linear groups. More generally, we discuss connections between the representations of symmetric groups and general linear groups. We describe some recent results, for small n, which explain 'fractals' and symmetry appearing in the context of decomposition numbers.




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