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d) Consider the Heisenberg group H3 generated by two elements a, 3 with the relation a3 = 2*/Ba. Let & := 2*1/3. Prove that the maps A and B : C3 C given by A(X,Y,Z) = (x.EY.&2). B(X,Y,Z) = (Y, Z, X) satisfy the relation of the Heisenberg group H3. (We thus say that Hz has a repre- sentation on C.) Also prove that in projective coordinates A, B give well defined, commutative, invertible maps on C (Here" well defined" means that the maps take points on C, to points on CX)