On the Representation Theory of the Finite Groups of Lie Type over an Algebraically Closed Field of Characteristic 0

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In this article we shall be describing the representation theory of a certain class of finite groups. In order to make clear the significance of this class of groups we recall the classification of the finite simple groups. In 1981 it was finally proved, after intensive effort by many workers over several decades, that every finite simple group must be one of the following: a cyclic group of prime order an alternating group of order 1/2! for ≥5 a group of Lie type over a finite field one of 26 sporadic simple groups The finite groups of Lie type are analogues over a finite field of the simple Lie groups over ℂ or ℝ.