Frank Lübeck   

Tables of Weight Multiplicities

This page provides data which were computed during the preparation of the following paper.

Lübeck, F., Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math., 4 (2001), p. 135--169

Here is a slightly updated preprint version of July 2001:
[BibTeX-Entry] [dvi-file (with hyperlinks)] [postscript-file] [pdf-file]

Additional data: groups of type D5 in characteristic 2 (containing ATLAS group O10(2)) - all 2-restricted weights,
groups of type D4 in characteristic 3 (containing ATLAS groups O8(3) and O8-(3)) - all 3-restricted weights,
the upper bound in case D4 was raised from 2000 to 7168 (the largest degree of the Weyl group of type E8),
groups of type C5 in characteristic 2 (containing ATLAS group Sp10(2)) - all 2-restricted weights.

Content

In the paper for each type of simple, simply connected, connected reductive algebraic group a bound is fixed and all irreducible representations of these groups in their defining characteristic p and of degree at most the given bound were determined. These representations are parameterized by highest weights, only those with p-restricted highest weights are listed. See the paper for more details.

For space reasons the paper lists only the parameterizing highest weights and the dimensions of the modules. Here we give a more detailed information and describe the weight multiplicities (characters) for all the representations of small rank groups appearing in the paper. To do this efficiently, we use the fact that the weight multiplicities are the same for all weights in a fixed orbit of the Weyl group in the weight lattice. Each such orbit contains a unique dominant weight (i.e., with non-negative coefficients as linear combination of the fundamental weights). We only give the weight multiplicities for dominant weights together with the length of the corresponding Weyl group orbit.

Update: (6/2006) The cases of type Al were extended to l < 21 and degree bounds (l+1)^4.

Here are the types of groups considered and the bounds. Click on the type to see the tables of weight multiplicities.

The Tables

Lie type   group names   bound
A2SL3400
A3SL4500
A4SL51000
A5SL62500
A6SL72800
A7SL84096
A8SL96561
A9SL1010000
A10SL1114641
A11SL1220736
A12SL1328561
A13SL1438416
A14SL1550625
A15SL1665536
A16SL1783521
A17SL18104976
A18SL19130321
A19SL20160000
A20SL21194481
B2Spin5300
B3Spin7700
B4Spin91000
B4Spin9[all 2-restricted weights in char. 2]
B5Spin112000
B6Spin134000
B7Spin155000
B8Spin177000
B9Spin198000
B10Spin2110000
B11Spin2312000
C3Sp61000
C4Sp82000
C5Sp102500
C5Sp10[all 2-restricted weights in char. 2]
C6Sp124000
C7Sp146000
C8Sp1610000
C9Sp1810000
C10Sp2010000
C11Sp2212000
D4Spin87168
D4Spin8[all 3-restricted weights in char. 3]
D5Spin103000
D5Spin10[all 2-restricted weights in char. 2]
D6Spin124000
D7Spin145000
D8Spin1610000
D9Spin1815000
D10Spin2018000
D11Spin2220000
E6E650000
E7E7100000
E8E8100000
F4F412000
G2G2500

Last updated: Mon Jul 29 10:22:24 2013 (CET)