Folding actions
R. Lawther · Bulletin of the London Mathematical Society · 1993
In this paper we begin by examining the action of E6(q) on the cosets of the subgroup F4(q): we give the rank and subdegrees, and show that it is multiplicity-free, that is, the constituents of the permutation character are all distinct. It is found that the suborbits correspond to conjugacy classes of A2(q); we seek to explain this using the concept of ‘folding actions’. This enables the related action of 2E6(q2 on F4(q) to be treated with little extra effort.