Abstracts Category : Other

The Brauer Complex and Decomposition Numbers of SymplecticGroups

by Ian Hogan

The decomposition problem for finite groups asks, fora given prime p dividing the order of the group, how can therestrictions of the ordinary characters to p-regular classes bewritten in terms of irreducible Brauer characters? We follow thedevelopment of L. Chastkofsky and J. E. Humphreys to construct theBrauer Complex of Sp(4,q) and Sp(6,q). The complex is an opensimplicial complex derived from the alcove geometry of theassociated affine Weyl group together with Deligne-Lusztigcharacter labels. The Deligne-Lusztig characters of Sp(4,q), odd q,were computed by B. Srinivasan and of Sp(6,q), even q, by F.Luebeck. As a consequence we gain information about thedecomposition matrices for these groups in definingcharacteristic.Advisors/Committee Members: White, Donald (Advisor).