| 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: (last updated 8/2018)
groups of type B4 in
characteristic 2 (containing ATLAS group
Spin9(2)=Sp8(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 F4 in
characteristic 2 - all 2-restricted weights,
groups of type A5 in
characteristic 2 - all 2-restricted weights,
groups of type A5 in
characteristic 3 - all 3-restricted weights,
groups of type D5 in characteristic 2
(containing ATLAS group O10(2)) - all 2-restricted weights,
groups of type C5 in
characteristic 2 (containing ATLAS group Sp10(2)) - all 2-restricted weights,
groups of type E6 in
characteristic 2 - 44 of the 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 |
|---|---|---|
| A2 | SL3 | 450 |
| A3 | SL4 | 1000 |
| A4 | SL5 | 3000 |
| A5 | SL6 | 7000 |
| A6 | SL7 | 9000 |
| A7 | SL8 | 15000 |
| A8 | SL9 | 20000 |
| A9 | SL10 | 30000 |
| A10 | SL11 | 30000 |
| A11 | SL12 | 35000 |
| A12 | SL13 | 40000 |
| A13 | SL14 | 50000 |
| A14 | SL15 | 50625 |
| A15 | SL16 | 65536 |
| A16 | SL17 | 100000 |
| A17 | SL18 | 150000 |
| A18 | SL19 | 130321 |
| A19 | SL20 | 160000 |
| A20 | SL21 | 194481 |
| B2 | Spin5 | 300 |
| B3 | Spin7 | 3000 |
| B4 | Spin9 | 4000 |
| B5 | Spin11 | 8000 |
| B6 | Spin13 | 15000 |
| B7 | Spin15 | 25000 |
| B8 | Spin17 | 40000 |
| B9 | Spin19 | 50000 |
| B10 | Spin21 | 60000 |
| B11 | Spin23 | 70000 |
| C3 | Sp6 | 2200 |
| C4 | Sp8 | 4000 |
| C5 | Sp10 | 7000 |
| C6 | Sp12 | 10000 |
| C7 | Sp14 | 25000 |
| C8 | Sp16 | 30000 |
| C9 | Sp18 | 40000 |
| C10 | Sp20 | 40000 |
| C11 | Sp22 | 12000 |
| D4 | Spin8 | 10000 |
| D5 | Spin10 | 15000 |
| D6 | Spin12 | 20000 |
| D7 | Spin14 | 25000 |
| D8 | Spin16 | 35000 |
| D9 | Spin18 | 70000 |
| D10 | Spin20 | 80000 |
| D11 | Spin22 | 100000 |
| E6 | E6 | 50000 |
| E7 | E7 | 100000 |
| E8 | E8 | 500000 |
| F4 | F4 | 30000 |
| G2 | G2 | 700 |
Last updated: Tue Oct 20 15:55:28 2020 (CET)