Intertwinings for Continuum Particle Systems: an Algebraic Approach
arXiv (Cornell University)(2023)
Abstract
We develop the algebraic approach to duality, more precisely to
intertwinings, within the context of particle systems in general spaces,
focusing on the 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).
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