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We use a quite concrete and simple realization of $\slq$ involving finitedifference operators. We interpret them as derivations (in the non-commutativesense) on a suitable graded algebra, which gives rise to the double of theprojective line as the non commutative version of the standard homogeneousspace.Comment: (5 pages - Plane TEX - SISSA-58/93/F

A borel-weil-bott approach to representations of sl q (2, ?)