latter. In particular, we have shown that certain brane configurations and intersections thereof which are asymptotically flat are mapped by the so-called shift transformation[@BPS1] to solutions that are locally isometric to $adS_k \xx E^l \xx S^m$, where $adS_k$ is the $k$-dimensional anti-de Sitter space, $E^l$ is the $l$-dimensional Euclidean space and $S^m$ is the $m$-dimensional sphere. Based on these considerations, it was further suggested in [@KSKS] that the actual symmetry group of M-theory is bigger than what one usually assumes, and allows for connections between spacetimes with different asymptotic group and different number of (non-compact) dimensions. The fact that these considerations lead to a microscopic derivation of the Bekenstein-Hawking entropy formula for $4d$ and $5d$ non-extremal black holes and organize many results on black hole entropy in a unifying way[@KSKS] strongly supports this point of view.

The proposed new dualities are rather surprising from the spacetime point of view. In a given spacetime, the particle states carry unitary irreducible representations (UIRs) of the spacetime group. If the spacetime is asymptotically flat then the particle states carry UIRs of the Poincaré group. After the duality transformation the spacetime changes to one which is asymptotically anti-de Sitter. So, now the particle states 