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Small degree representations of finite Chevalley groups in defining characteristic. (English) Zbl 1053.20008
Summary: The author determines, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank \(l\), this bound is proportional to \(l^3\), and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

MSC:
20C33 Representations of finite groups of Lie type
20C40 Computational methods (representations of groups) (MSC2010)
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
Software:
EDIM; CHEVIE
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References:
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