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Intertwinings for Continuum Particle Systems: an Algebraic Approach
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral operators indexed by test functions and we use them to construct unitary operators, which act as self-intertwiners for some Markov processes having the Pascal process's law as a reversible measure. We show that such unitaries relate to generalized Meixner polynomials. Our primary results are continuum counterparts of results in the discrete setting obtained by Carinci, Franceschini, Giardinà, Groenevelt, and Redig (2019).
Keywords: algebraic approach to stochastic duality, intertwining; inclusion process, Lie algebra $\mathfrak{su}(1,1)$
Mots-clés : orthogonal polynomials. 
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     author = {Simone Floreani and Sabine Jansen and Stefan Wagner},
     title = {Intertwinings for {Continuum} {Particle} {Systems:} an {Algebraic} {Approach}},
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}
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Simone Floreani; Sabine Jansen; Stefan Wagner. Intertwinings for Continuum Particle Systems: an Algebraic Approach. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a45/

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