On m-tuples of nilpotent 2 × 2 matrices over an arbitrary field.

The algebra of GLn-invariants of m-tuples of n × n matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators of polynomial invariants are not known even for a pair of 2 × 2 matrices. Working over an arbitrary field we classified all GL2-orbits on m-tuples of 2 × 2 nilpotent matrices for all m > 0. As a consequence, we obtained a minimal separating set for the algebra of GL2-invariant polynomial functions of m-tuples of 2 × 2 nilpotent matrices. We also described the least possible number of elements of a separating set for an algebra of invariant polynomial functions over a finite field. [ABSTRACT FROM AUTHOR]