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

TL;DR

This paper investigates the genetic code's degeneracy through the lens of Lie superalgebras, providing a classification of codon representations as a step toward understanding the underlying symmetry breaking.

Contribution

It introduces the use of classical Lie superalgebras to model the genetic code's degeneracy, offering a complete list of typical codon representations.

Findings

Classified all typical 64-dimensional codon representations

Proposed Lie superalgebras as a framework for genetic code symmetry

Set the stage for analyzing multiplet structures in future work

Abstract

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