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Data for Finite Groups of Lie Type and Related Algebraic Groups

The following results are answers to questions I got from various people. Tell me if you have any comments, suggestions, further questions, ...

This part of these web pages will be enlarged significantly. Currently I'm writing a documentation of the theoretical and algorithmic background of the results presented here. Hopefully, at some stage I will turn my large collection of computer programs into publicly available software packages.

Possible topics for this section are all sorts of information on conjugacy classes, structures of certain subgroups and representations. The emphasis is on results of computations, in particular for the series of exceptional groups of Lie type.

To get started we have for now:

• Numbers of conjugacy classes, semisimple classes, semisimple elements, ... in some series of groups.
• All degrees of complex irreducible representations and their multiplicities for many series of groups of semisimple rank less than 9.
• Tables of weight multiplicities of small degree representations in defining characteristic.
• A description of the conjugacy classes of elements of orders 2 and 3 in exceptional groups of Lie type.
• Conjugacy class lenghts and character degrees for ²E₆(2).
• Conjugacy class lenghts and character degrees for E₇(2).
• Conjugacy class lenghts and character degrees for E₈(2).
• extraGenTabGLGU.tar.gz is an archive containing the generic character tables of GL_n(q) and GU_n(q) for n = 4,5,6. These extra tables can be used with both versions of cheviem (that is with MapleV.3, or with Maple 8 and higher, see the CHEVIE page. Just unpack the archive in the tables subdirectory of your cheviem installation.
• Permutation representations, each on 16575 points, of the groups O_8^+(4):3 (328 kB) and O_8^+(4):S_3 (436 kB) as GAP-readable files.
• Permutation representations of O_8^+(5) (0.7MB), O_8^+(5).3 (1.0MB) and O_8^+(5).S_3 (1.3MB) on 117000 points and permutation representations of 2^2.O_8^+(5) = Spin_8(5) (1.4MB), 2^2.O_8^+(5).3 = Spin_8(5).3 (2.1MB) and 2^2.O_8^+(5).S_3 = Spin_8(5).S_3 (2.8MB) on 234000 points. The files are gzip'ed and GAP-readable.

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Last updated: Fri Mar 23 15:13:40 2007 (CET)