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Dear Forum,

I need to be able to obtain the action of the Projective Unitary

group PGU(n+1,q) on the vectors of the Projective Space PG(n,q^2).

[actually, I need this for q=5 and n=3, but I expect the solution

to be valid for any suitable n,q]

Here there is my question:

What is the sesquilinear form respected by the group PGU(n+1,q),

assuming that the vectors of PG(3,q^2) are enumerated in the order

given by

Orbit(GL(4,q^2),Z(q)^0*[1,0,0,0],OnLines) ?

[or, conversely, in what order may I enumerate the elements of

PG(n,q^2) if I wish PGU(n+1,q) to be the group preserving the

sesquilinear form induced by the identity matrix?]

Thanks in advance.

lg

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