We describe an elementary algorithm for expressing, as explicit formulae in
tractor calculus, the conformally invariant GJMS operators due to C.R. Graham
et alia. These differential operators have leading part a power of the
Laplacian. Conformal tractor calculus is the natural induced bundle calculus
associated to the conformal Cartan connection. Applications discussed include
standard formulae for these operators in terms of the Levi-Civita connection
and its curvature and a direct definition and formula for T. Branson's
so-called Q-curvature (which integrates to a global conformal invariant) as
well as generalisations of the operators and the Q-curvature. Among examples,
the operators of order 4, 6, and 8 and the related Q-curvatures are treated
explicitly. The algorithm exploits the ambient metric construction of Fefferman
and Graham and includes a procedure for converting the ambient curvature and
its covariant derivatives into tractor calculus expressions. This is partly
based on "Standard tractors and the conformal ambient metric construction" (A.
Cap and A.R. Gover, math.DG/0207016), where the relationship of the normal
standard tractor bundle to the ambient construction is described.Comment: 42 pages. No figures. Record of changes: V1, 15 January 2002:
Original posting. V2, 17 January 2002: Changing comment fields. Leaving
abstract and text of article unchanged. V3, 1 February 2003: Minor changes
and typographical corrections throughout articl
