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In this note, we formulate an observation that "almost all" irreducibleordinary characters of finite groups of Lie type remain irreducible whenrestricted to the derived subgroups. To see this, key ingredients are someasymptotic results for conjugacy classes of finite groups of Lie type andstrongly regular semisimple elements in dual groups.

Restrictions of irreducible characters of finite groups of Lie type to derived subgroups and regular semisimple elements