Intertwinings for Continuum Particle Systems: an Algebraic Approach
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the (1, 1) current algebra. We introduce raising, lowering, and neutral operators indexed by test functions, and we use them to construct unitary opera...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212261 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Intertwinings for Continuum Particle Systems: an Algebraic Approach. Simone Floreani, Sabine Jansen and Stefan Wagner. SIGMA 20 (2024), 046, 21 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the (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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| ISSN: | 1815-0659 |