Orthogonal Dualities of Markov Processes and Unitary Symmetries

@article{Carinci2019OrthogonalDO,
  title={Orthogonal Dualities of Markov Processes and Unitary Symmetries},
  author={Gioia Carinci and Chiara Franceschini and Cristian Giardin{\`a} and Wolter G. M. Groenevelt and Frank Redig},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2019}
}
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries we provide two equivalent expressions that are related by the Baker-Campbell-Hausdorff formula. The first expression is the exponential of an anti Hermitian operator and thus is unitary by inspection; the… 
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