The authors determine all the absolutely irreducible representations of degree up to 250 of quasi-simple finite groups, excluding groups that are of Lie type in their defining characteristic. Additional information is also given on the Frobenius-Schur indicators and the Brauer character fields of the representations.

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Abstract. The distribution of the unipotent modules (in nondefining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph of an integrable module for a certain quantum group. Evidence for our conjectures is presented, as well as proofs for some of their consequences for the crystal graphs involved. In the course of our work we also generalize Harish-Chandra theory for some of the finite classical groups, and we introduce their Harish-Chandra branching graphs.

This paper contains corrections to the tables of low-dimensional representations of quasi-simple groups published in the paper, 'Lowdimensional representations of quasi-simple groups', LMS Journal of Computation and Mathematics 4 (2001) 22-63.In our paper 'Low-dimensional representations of quasi-simple groups', we determine all the absolutely irreducible representations of quasi-simple groups of dimension at most 250, excluding those of groups of Lie type in their defining characteristic.Martin Liebeck has kindly pointed out to us three omissions in our tables: the 12-and 13-dimensional representations of the group L 3 (3), and the 248-dimensional representations of L 4 (5) in characteristic 2.When checking our arguments and calculations we realized that in fact all the representations of L 3 (3) were missing, as well as the representations of L 4 (5) of dimension exceeding 247.The absolutely irreducible representations of L 3 (3) can be found in the modular Atlas [7]. This leads to the first part of Table 1 below. The absolutely irreducible representations of L 4 (5) of degree up to 247 were classified by Guralnick and Tiep [3], and are contained in the original table. From the proofs given by Tiep

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