A borel-weil-bott approach to representations of slq(2, C)

We use a quite concrete and simple realization of slq(2, C) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the 'noncommutative' scheme P1 II P1* as the counterpart of the standard P1 = Sl(2, C)/B. © 1993 Kluwer Academic Publishers.