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This is a talk in pure group theory. The (irreducible, finite-dimensional) representations of SL(2,K) as an algebraic group are well-known: they are the various K[X^d, X^(d-1)Y, ..., Y^d], and the proof uses Lie algebras. Now dropping all form of "geometric" information (i.e., the algebraic group structure, so also the Lie algebra), we may ask whether these objects can be identified not only as representations of SL(2,K), but even as SL(2,K)-modules. We shall discuss partial results and open questions.