More on matrix semigroup homomorphisms Original Research Article

We study non-degenerate irreducible homomorphisms from the multiplicative semigroup of all 2-by-2 complex matrices to the semigroup of n-by-n complex matrices. If such a homomorphism maps a cyclic unipotent to a cyclic unipotent, it is the composition of a symmetric power, a field homomorphism used entrywise, and a matrix conjugation. In the case n=4 we characterise all non-degenerate irreducible homomorphisms.