My research project takes part of a bigger international project. Its aim consists in the classification of the admissible representations of reductive groups over local fields.
C. Bushnell and Ph. Kutzko obtained a very satisfactory result with the group GLN(F), F a local field, and it has been conjectured that their construction can be generalized in the case of the anisotropic interior forms of GLN (i.e. groups like GLN(D), D a local division algebra). In my thesis, I proved that we can deal with the case Dx=GL1(D) and rediscover the already existing Zink's classification.
My project is to widen my thesis work to the case N>2 in collaboration with C. Bushnell.
We know very little about the group GLN(D) and more generally about the nonsplit groups. New very interesting phenomenons migh appear here. That is why it study is of great interest.