Adventures in Invariant Theory
  We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics. 
P. D. Jarvis and J. G. Sumner
q-bio.QM math.GR math.ST q-bio.PE quant-ph stat.TH