# zbMATH — the first resource for mathematics

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
EDIM; CHEVIE
Full Text:
##### References:
 [1] Curtis, Methods of representation theory · JFM 06.0598.01 [2] DOI: 10.1007/BF01190329 · Zbl 0847.20006 [3] Benson, Representations and cohomology 30 (1991) [4] Steinberg, Mem. Amer. Math. Soc. 80 (1968) [5] DOI: 10.1070/SM1988v061n01ABEH003200 · Zbl 0669.20035 [6] Moody, Bull. Amer. Math. Soc. 1 pp 237– [7] Lübeck, J. Sym bolic Comput. [8] Kleidman, The subgroup structure of the finite classical groups 129 (1990) · Zbl 0697.20004 [9] Jantzen, Pure Appl. Math. [10] Jantzen, J. Reine Angew. Math. 290 pp 117– [11] Humphereys, Finite simple groups II pp 259– [12] Jansen, An atlas of Brauer characters (1995) · Zbl 0831.20001 [13] Hiss, LMS J. Comput. Math. 4 pp 22– · Zbl 0979.20012 [14] Gilkey, Geom. Dedicata 25 pp 407– [15] Burgoyne, Representation theory of finite groups and related topics pp 13–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.