Abstract :
We prove that the permutation representation of the finite orthogonal group Ωε(n, q), where ε = +
or −, on the set of anisotropic lines is multiplicity-free, if q is a power of 2 and n 6 is even.
This result is established by giving a description of orbitals of this action. The rank of this action
is (q2 + 2q)/2 if ε = + and n = 6, and (q2 + 2q + 2)/2 otherwise. Moreover, we compute the
subdegrees of the orbitals of Ωε(n, q).
