  We present the complete toroidal compactification of the Gauss-Bonnet
Lagrangian from D dimensions to (D-n) dimensions. Our goal is to investigate
the resulting action from the point of view of the "U-duality" symmetry
SL(n+1,R) which is present in the tree-level Lagrangian when D-n=3. The
analysis builds upon and extends the investigation of the paper
[arXiv:0706.1183], by computing in detail the full structure of the
compactified Gauss-Bonnet term, including the contribution from the dilaton
exponents. We analyze these exponents using the representation theory of the
Lie algebra sl(n+1,R) and determine which representation seems to be the
relevant one for quadratic curvature corrections. By interpreting the result of
the compactification as a leading term in a large volume expansion of an
SL(n+1,Z)-invariant action, we conclude that the overall exponential dilaton
factor should not be included in the representation structure. As a
consequence, all dilaton exponents correspond to weights of sl(n+1,R), which,
nevertheless, remain on the positive side of the root lattice.
