Descriptions of the unary polynomial functions on Frobenius complements
and formulas for their numbers are given in [#!Ma:TPFO!#]. This involves
a study of functions on SL. More generally in [#!AM:PFAE!#],
E. Aichinger and P. Mayr described the polynomial functions and endomorphism
near-rings on subgroups of the general linear groups that contain the
special linear groups. In his Ph.D.-thesis, P. Mayr gave an account of
polynomial functions on all non-solvable classical linear groups (unitary,
symplectic, orthogonal).
The results on polynomial functions found widespread interest at international conferences on group theory and universal algebra. Also people from algebraic geometry and topology could be won to collaborate on functions on infinite linear groups [#!LM:ATPO!#].