Identities for matrix invariants of the symplectic group

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.