GenericDecMats
This repository gives access to the generic decomposition matrices of various groups of Lie type.
Currently the following use cases are supported.

The Gapjm.jl package provides functionality for generic decomposition matrices.

The generic decomposition matrices can be read into Oscar.jl, its matrices and polynomials are used then.

There is also a GAP 4 interface, read
init.g
into a GAP session in order to provide functions for loading, displaying, and testing the matrices.
The interfaces to Gapjm.jl and Oscar.jl can be used in the same Julia session.
There is a preliminary printout version of the data; both the location and the format will be changed.
The data (in the data
subdirectory) have been provided by Gunter Malle.
References
[CDR20] Craven, D. A., Dudas, O. and Rouquier, R., Brauer trees of unipotent blocks, J. Eur. Math. Soc. (JEMS), 22 (9) (2020), 2821–2877.
[Dud13] Dudas, O., A note on decomposition numbers for groups of Lie type of small rank, J. Algebra, 388 (2013), 364–373.
[DM15] Dudas, O. and Malle, G., Decomposition matrices for lowrank unitary groups, Proc. Lond. Math. Soc. (3), 110 (6) (2015), 1517–1557.
[DM16] Dudas, O. and Malle, G., Decomposition matrices for exceptional groups at d=4, J. Pure Appl. Algebra, 220 (3) (2016), 1096–1121.
[DM19] Dudas, O. and Malle, G., Bounding HarishChandra series, Trans. Amer. Math. Soc., 371 (9) (2019), 6511–6530.
[DM] Dudas, O. and Malle, G., Decomposition matrices for groups of Lie type in nondefining characteristic, arXiv:2001.06395.
[DR14] Dudas, O. and Rouquier, R., Coxeter orbits and Brauer trees III, J. Amer. Math. Soc., 27 (4) (2014), 1117–1145.
[FS84] Fong, P. and Srinivasan, B., Brauer trees in GL(n,q), Math. Z., 187 (1) (1984), 81–88.
[FS90] Fong, P. and Srinivasan, B., Brauer trees in classical groups, J. Algebra, 131 (1) (1990), 179–225.
[Gec91] Geck, M., Generalized GelʹfandGraev characters for Steinberg's triality groups and their applications, Comm. Algebra, 19 (12) (1991), 3249–3269.
[GH97] Geck, M. and Hiss, G., Modular representations of finite groups of Lie type in nondefining characteristic, in Finite reductive groups (Luminy, 1994), Birkhäuser Boston, Boston, MA, Progr. Math., 141 (1997), 195–249.
[GHM94] Geck, M., Hiss, G. and Malle, G., Cuspidal unipotent Brauer characters, J. Algebra, 168 (1) (1994), 182–220.
[HN14] Himstedt, F. and Noeske, F., Decomposition numbers of SO_7(q) and Sp_6(q), J. Algebra, 413 (2014), 15–40.
[HL98] Hiss, G. and Lübeck, F., The Brauer trees of the exceptional Chevalley groups of types F_4 and ^2E_6, Arch. Math. (Basel), 70 (1) (1998), 16–21.
[HLM95] Hiss, G., Lübeck, F. and Malle, G., The Brauer trees of the exceptional Chevalley groups of type E_6, Manuscripta Math., 87 (1) (1995), 131–144.
[Jam90] James, G., The decomposition matrices of GL_n(q) for n ≤ 10, Proc. London Math. Soc. (3), 60 (2) (1990), 225–265.
[Mal] Malle, G., Computed directly (in principle known from MR1031453 [Jam90]).
[Miy08] Miyachi, H., Rouquier blocks in Chevalley groups of type E, Adv. Math., 217 (6) (2008), 2841–2871.
[OW98] Okuyama, T. and Waki, K., Decomposition numbers of Sp(4,q), J. Algebra, 199 (2) (1998), 544–555.
[OW02] Okuyama, T. and Waki, K., Decomposition numbers of SU(3,q^2), J. Algebra, 255 (2) (2002), 258–270.
[Sha89] Shamash, J., Brauer trees for blocks of cyclic defect in the groups G_2(q) for primes dividing q^2 ± q + 1, J. Algebra, 123 (2) (1989), 378–396.