  The general linear group acts on the space of several linear maps on the
vector space as the basis change. Similarly, we have the actions of the
orthogonal and symplectic groups. Generators and identities for the
corresponding polynomial invariants over a characteristic zero field were
described by Sibirskii, Procesi and Razmyslov in 1970s. In 1992 Donkin started
to transfer these results to the case of infinite fields of arbitrary
characteristic. We completed this transference for fields of odd characteristic
by establishing identities for the symplectic matrix invariants over infinite
fields of odd characteristic.
