Identities for matrix invariants of the symplectic group

TL;DR

This paper extends the understanding of polynomial invariants for symplectic groups over infinite fields of odd characteristic, completing a transfer of classical results to this broader setting.

Contribution

It establishes identities for symplectic matrix invariants over infinite fields of odd characteristic, filling a gap in the transfer of classical invariant theory results.

Findings

Identities for symplectic matrix invariants over odd characteristic fields are established.

Completes the transfer of invariant descriptions from characteristic zero to odd characteristic fields.

Advances the understanding of polynomial invariants for symplectic groups in broader algebraic settings.

Abstract

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.