Orthogonal Stochastic Duality Functions from Lie Algebra Representations.

J Stat Phys 2019 19;174(1):97-119. Epub 2018 Oct 19.

Technische Universiteit Delft, DIAM, PO Box 5031, 2600 GA Delft, The Netherlands.

We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and . Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.

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http://dx.doi.org/10.1007/s10955-018-2178-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383627PMC
October 2018

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