e8_gap.at

e8_gap_table

this table determines numbering of W(E8) irreps used in springer_table_E8

the order of the columns (conjugacy classes) is that used by GAP

a list of 112 rows, one for each irred. character

e8_gap_centralizer_sizes

sizes of the 112 classes, in GAP order

e8_gap_orders

112 orders of class elements, in GAP order

e8_gap_classes

conjugacy class labels, in GAP order

e8_gap_class_nr

label to GAP class number

(gap_power_2, gap_power_3, gap_power_5, gap_power_7)

e8_gap_profile

Finally make a 5x112 matrix whose columns, corresponding to conjugacy classes,
are all distinct. Since these 5 statistics are easy to compute for every
element of W(E8), this will allow mapping data from the GAP numbering of
conjugacy classes to any ordering we prefer. In class_tables.at We define a
natural ordering by lexicographically listing the orbit types in the action on
roots, and in character_tables_E8.at we compute said mapping, and then import
the data from the above tables into the CharacterTable for E8.

of shape (5,112 with all columns distinct