Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

TL;DR

This paper explores how certain Lie superalgebras, specifically osp(5|2), can model the degeneracy patterns of the genetic code through branching schemes of codon representations, offering a mathematical framework for genetic code structure.

Contribution

It introduces specific branching schemes for typical codon representations of Lie superalgebras that reproduce the genetic code's degeneracy patterns, expanding previous models.

Findings

Identified three branching schemes matching genetic code degeneracies

Used orthosymplectic algebra osp(5|2) for modeling

Detailed symmetry breaking patterns during representation branching

Abstract

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.