  The classical-quantum duality at the basis of quantum theory is here extended
to the Planck scale domain. The classical/semiclassical gravity (G) domain is
dual (in the precise sense of the classical-quantum duality) to the quantum (Q)
elementary particle domain through the Planck scale. This duality is universal.
From the gravity and quantum variables (G, Q), we define new (QG) quantum
gravity variables QG = (1/2) (G + Q) which include all (classical,
semiclassical and quantum gravity) domains and the elementary particle domain
passing by the Planck scale. Two values of G or Q variables are necessary for
each variable QG. The complete analytic extension of the QG variables is
performed. This allows us to reveal the classical-quantum duality of the
Schwarzschild-Kruskal space-time: The exterior regions are
classical/semiclassical while the interior is totally quantum, its boundaries
being the Planck scale. Exterior and interior lose their difference near the
horizon which turns to be quantum dressed, " l'horizon habille' ". QG variables
are naturally invariant under G --> Q and conversely. Space-time reflections,
antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry,
which also shed insight into the global properties of the Kruskal manifold and
its present renewed interest...(Abridged)
