A crystal base for the genetic code
Résumé
The quantum enveloping algebra U_q(sl(2) \oplus sl(2)) in the limit q \to 0 is proposed as a symmetry algebra for the genetic code. In this approach the triplets of nucleotids or codons in the DNA chain are classified in crystal bases, tensor product of U_{q \to 0}(sl(2) \oplus sl(2)) representations. Such a construction might be compared to the baryon classification from quark building blocks in elementary particles physics, one of the main differences standing in the property of a crystal base to provide a natural order in the state constituents, this order being crucial in the codon. Then an operator ensuring the correspondence codon/amino-acid can be constructed out of the above algebra. It will be called the reading operator, and be such that two codons relative to the same (resp. different) amino-acid(s) acquire the same (resp. different) eigenvalue(s).