Minimizing representations over number fields

AbstractFinding minimal fields of definition for representations is one of the most important unsolved problems of computational representation theory. While good methods exist for representations over finite fields, it is still an open question in the case of number fields. In this paper we give a practical method for finding minimal defining subfields for absolutely irreducible representations. We illustrate the new algorithm by determining a minimal field for each absolutely irreducible representation of Sz(8)