Lie Superalgebras and the Multiplet Structure of the Genetic Code I: Codon Representations

摘要

It has been proposed that the degeneracy of the genetic code,i.e., thephenomenon that different codons (base triplets) of DNA are transcribed intothe same amino acid, may be interpreted as the result of a symmetry breakingprocess. In the initial work of Hornos & Hornos this picture was developed inthe framework of simple Lie algebras. Here, we explore the possibility ofexplaining the degeneracy of the genetic code using basic classical Liesuperalgebras, whose representation theory is sufficiently well understood, atleast as far as typical representations are concerned. In the present paper, wegive the complete list of all typical codon representations (typical 64-dimensional irreducible representations), whereas in the second part, we shallpresent the corresponding branching rules and discuss which of them reproducethe multiplet structure of the genetic code.