SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE

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Products of conjugacy classes and fixed point spaces (2010, unknown): “Thus, the multiplicity of any linear character of T in χ|T is at most χ(1) + 30|T | |T | = χ(1) |T | + 30 ≤ χ(1) q8 as claimed, since χ(1) > q(28) by [39].”
The Ore conjecture (2010, unknown): “Proof (i) This follows from [32].”
Representations of finite groups of Lie type (2008, unknown): “[50] F. Lübeck, Smallest degrees of representations of exceptional groups of Lie type, Comm. Algebra 29 (2001), 2147− 2169.”
Primes dividing the degrees of the real characters (2008, background): “On the other hand, Irr(S) contains a unique character χ2 of smallest degree q� 12(q) ,c f. [ 20 ].”
Rational irreducible characters and rational conjugacy classes in finite groups (2007, background): “For these groups, it is shown in [20] that S has a unique non-trivial (unipotent) irreducible character of smallest degree.”