Lie superalgebras and the multiplet structure of the genetic code. I. Codon representations

It has been proposed by Hornos and Hornos [Phys. Rev. Lett. 71, 4401-4404 ( 1993)] that the degeneracy of the genetic code, i.e., the phenomenon that d ifferent codons (base triplets) of DNA are transcribed into the same amino acid, may be interpreted as the result of a symmetry breaking process. In t heir work, this picture was developed in the framework of simple Lie algebr as. Here, we explore the possibility of explaining the degeneracy of the ge netic code using basic classical Lie superalgebras, whose representation th eory is sufficiently well understood, at least as far as typical representa tions are concerned. In the present paper, we give the complete list of all typical codon representations (typical 64-dimensional irreducible represen tations), whereas in the second part, we shall present the corresponding br anching rules and discuss which of them reproduce the multiplet structure o f the genetic code. (C) 2000 American Institute of Physics. [S0022-2488(00) 06205-8].