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ADVENTURES IN INVARIANT THEORY

Part of: Forms and linear algebraic groups Algebraic combinatorics Mathematical biology in general

Published online by Cambridge University Press:  15 December 2014

P. D. JARVIS  and
J. G. SUMNER
P. D. JARVIS*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37 GPO, Hobart Tas 7001, Australia email Peter.Jarvis@utas.edu.au, Jeremy.Sumner@utas.edu.au
J. G. SUMNER
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37 GPO, Hobart Tas 7001, Australia email Peter.Jarvis@utas.edu.au, Jeremy.Sumner@utas.edu.au
*
✉Peter.Jarvis@utas.edu.au
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Abstract

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We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualized via two case studies, arising from our recent work: entanglement invariants for characterizing 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.

Keywords

group characterinvariantplethysmSchur functionentanglementqubittanglesquanglequartetgeneral Markov model

MSC classification

Primary: 05E05: Symmetric functions and generalizations
Secondary: 11E57: Classical groups 81P68: Quantum computation 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 2 , October 2014 , pp. 105 - 115
Copyright
Copyright © 2014 Australian Mathematical Society 

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