  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, Giardin\`a, Groenevelt, and Redig (2019).
