Self-Duality of Markov Processes and Intertwining Functions

@article{Franceschini2018SelfDualityOM,
  title={Self-Duality of Markov Processes and Intertwining Functions},
  author={Chiara Franceschini and Cristian Giardin{\`a} and Wolter G. M. Groenevelt},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2018},
  volume={21},
  pages={1-21}
}
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two representations of a certain Lie algebra is the self-duality function of a (Markov) operator. In concrete terms, the two representations are associated to two operators in interwining relation. The self-dual operator, which arise from an appropriate symmetric… 
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