Adventures in Invariant Theory

Abstract

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.

12 pp, includes supplementary discussion of examples

References in corpus (5)

• Quantum entanglement
• Quantifying entanglement resources
• New branching rules induced by plethysm
• Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model
• The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C)

Cited by in corpus (2)

• Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model
• Systematics and symmetry in molecular phylogenetic modelling: perspectives from physics