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Orthogonal Stochastic Duality Functions from Lie Algebra Representations

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 [Formula: see text] -representations, which provides (generalized) orthogonality relations for the duality fun...

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Autor principal: Groenevelt, Wolter
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383627/
https://www.ncbi.nlm.nih.gov/pubmed/30872864
http://dx.doi.org/10.1007/s10955-018-2178-7
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author Groenevelt, Wolter
author_facet Groenevelt, Wolter
author_sort Groenevelt, Wolter
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description 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 [Formula: see text] -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and [Formula: see text] . 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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spelling pubmed-63836272019-03-12 Orthogonal Stochastic Duality Functions from Lie Algebra Representations Groenevelt, Wolter J Stat Phys Article 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 [Formula: see text] -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and [Formula: see text] . Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes. Springer US 2018-10-19 2019 /pmc/articles/PMC6383627/ /pubmed/30872864 http://dx.doi.org/10.1007/s10955-018-2178-7 Text en © Springer Science+Business Media, LLC, part of Springer Nature 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Groenevelt, Wolter
Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title_full Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title_fullStr Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title_full_unstemmed Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title_short Orthogonal Stochastic Duality Functions from Lie Algebra Representations
title_sort orthogonal stochastic duality functions from lie algebra representations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383627/
https://www.ncbi.nlm.nih.gov/pubmed/30872864
http://dx.doi.org/10.1007/s10955-018-2178-7
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