Reconstruction of universal Drinfeld twists from representations.

Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and have appeared in numerous applications, no twist for a semisimple quantum enveloping algebra has ever been computed. It is argued that universal twists can be reconstructed from their well-known representations. A method to reconstruct an arbitrary element of the enveloping algebra from its irreducible representations is developed. For the twist this yields an algebra valued generating function to all orders in the deformation parameter, expressed by a combination of basic and ordinary hypergeometric functions. It is shown how the generating function can be expanded to the formal power series of the twist. An explicit expression for the universal twist of su(2) is given up to third order. [ABSTRACT FROM AUTHOR]