0534685 20240103224744.520201119235959.9 978-981-12-0608-5 978-981-12-0610-8 1793-0758 10.1142/9789811206092_0003 New Jersey Hackensack: World Scientific 2020 69 s. 364 P Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore Genealogies of Interacting Particle Systems 38 cav_un_epca*0535088978-981-120-608-581-150SingapureWorld Scientific2020 interacting particle system duality intertwining representations of Lie algebras cav_un_auth*0244526 Sturm A. DE 33 cav_un_auth*0217893 Swart Jan M. UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ 33 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0399597 Völlering F. DE 34 http://library.utia.cas.cz/separaty/2020/SI/swart-0534685.pdf GA16-15238S GA ČR CZ cav_un_auth*0334217 This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise ap- proach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent sug- gestion by Giardinà, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations of Lie algebras that is crucial for this approach. We also discuss older work by Lloyd and Sudbury on duality functions of product form and the relation between intertwining and duality. cav_un_auth*0399598 Genealogies of Interacting Particle Systems 20170717 20170818 Singapore SG BA 10000 10100 10103 2021 3 RVO:67985556 http://hdl.handle.net/11104/0313197 S 2020 M 2020 New Jersey Hackensack: World Scientific 978-981-12-0608-5 978-981-12-0610-8 SCOPUS PUBMED WOS cav_un_epca*0535088 Genealogies of Interacting Particle Systems 978-981-120-608-5 81 150 Singapure World Scientific 2020 Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 38