MASSLESSNESS IN N-DIMENSIONS

We determine the representations of the ''conformal'' group SO0(2, n), the restriction of which on the ''Poincare'' subgroup <(SO)over bar>( 0) (l, n - 1).T-n are unitary irreducible. We study their restrictions to the ''De Sitter'' subgroups <(SO)over bar>0 (1, n) and <(SO)over b ar>(0)(2, n - 1) (they remain irreducible or decompose into a sum of t wo) and the contraction of the latter to ''Poincare''. Then we discuss the notion of masslessness in n dimensions and compare the situation for general n with the well-known case of 4-dimensional space-time, sh owing the specificity of the latter.