Carl Riehm
McMaster University
Hamilton, Ontario

This paper deals with orthogonal, symplectic and unitary representations of finite groups over
finite, local and global fields. The main problems treated are the determination of the
symmetric, skew-symmetric and Hermitian forms which are invariant under a linear
representation of a finite group, the number of equivariant equivalence classes, and
conditions on the representations and the group under which two representations of the same
type (orthogonal, symplectic or unitary) are equivalent if and only if they are equivalent as
linear representations.

This is a reprint, to appear in the Transactions of the AMS.