Orthogonal stochastic duality functions from Lie algebra representations

DOI10.1007/S10955-018-2178-7zbMATH Open1439.82032arXiv1709.05997OpenAlexW3105821085WikidataQ64944195 ScholiaQ64944195MaRDI QIDQ1730956

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Publication date: 6 March 2019

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Abstract: 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 $mathfraksu(1,1)$. Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.

Full work available at URL: https://arxiv.org/abs/1709.05997

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