Représentations orthogonales et symplectiques sur un corps de
caractéristique différente de 2

Bruno Kahn
CNRS - Institut de Mathématiques de Jussieu

In this paper, we study linear, orthogonal and symplectic representations
of finite groups over an arbitrary field of characteristic different
from 2. Our aim is to classify those representations of a 2-group which
are irreducible and primitive (i.e. not induced from any proper subgroup).
This aim is not completely achieved in the orthogonal and symplectic cases
because scalars not defined over the base field provide trivial examples
of large-dimensional primitive representations, but we are able to
complete the classification for the weaker issue of linear representations
of orthogonal or symplectic types which are irreducible and not induced
from any proper representation of this type. While the results are simple
to state and essentially classical when the base field contains a square
root of -1, the general case is quite complex and involves a large number
of cases.

Status: preprint.