Dade's Conjecture in the Finite Special Unitary Groups
thesisposted on 10.12.2012 by Katherine A. Bird
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
The theory of p-modular representations of a finite group G for a fixed prime number p was developed by Richard Brauer. One of the main problems in this theory is to classify the p-blocks which form a partition of the set of characters of G. Dade conjectured a formula for the number of characters in a block in terms of characters in blocks in certain subgroups called p-local subgroups of G. This conjecture has been verified for groups such as the finite general linear, special linear, and unitary groups over a field of characteristic p. In this thesis we verify the conjecture for the finite special unitary groups over a field of characteristic p.