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 this article from January 2016:
[BibTeX-Entry] [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,
groups of type C5 in characteristic 2 (containing ATLAS group Sp10(2)) - all 2-restricted weights.
groups of type B4 in characteristic 2 (containing ATLAS group Spin9(2)=Sp8(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.

Update: (6/2017) Data were recomputed with (sometimes much) larger bounds than in the paper mentioned above.

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
A2SL3450
A3SL41000
A4SL53000
A5SL67000
A6SL79000
A7SL815000
A8SL920000
A9SL1030000
A10SL1130000
A11SL1235000
A12SL1340000
A13SL1450000
A14SL1550625
A15SL1665536
A16SL1783521
A17SL18150000
A18SL19130321
A19SL20160000
A20SL21194481
B2Spin5300
B3Spin72000
B4Spin94000
B5Spin118000
B6Spin1315000
B7Spin1525000
B8Spin1740000
B9Spin1950000
B10Spin2160000
B11Spin2370000
C3Sp62200
C4Sp84000
C5Sp107000
C6Sp1210000
C7Sp1425000
C8Sp1630000
C9Sp1840000
C10Sp2040000
C11Sp2212000
D4Spin810000
D5Spin1015000
D6Spin1220000
D7Spin1425000
D8Spin1635000
D9Spin1870000
D10Spin2080000
D11Spin22100000
E6E650000
E7E7100000
E8E8500000
F4F430000
G2G2700

Zuletzt geändert: Fr 18.08.2017, 21:54:06 (UTC)