Radha Kessar

Rationality and quaternion blocks

To each indecomposable factor (block) of a finite group algebra over a field of positive characteristic p is associated a conjugacy class of finite p-subgroups of the group called the defect groups of the block. A conjecture of Donovan predicts that up to Morita equivalence there are only finitely many blocks with a given isomorphism class of defect group. Karin Erdmann's work from the late 1980s yields an almost complete solution of this conjecture in the case that the defect group is of tame representation type. There is only class of tame representation type which is still open - that of quaternion defect group and two simple modules. I will report on ongoing joint work with Charles Eaton, Florian Eisele, Markus Linckelmann and Mandi Schaeffer Fry on this open case.