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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10219 |
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| _version_ | 1866912706659876864 |
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| author | Ejsmont, Wiktor Hęćka-Jędraszczyk, Patrycja |
| author_facet | Ejsmont, Wiktor Hęćka-Jędraszczyk, Patrycja |
| contents | The double Fock space of type B was introduced in 2023 by Bożejko and Ejsmont (\cite{BE23}). In this article, we show the acting of Poisson type operators in that space. For this purpose, we define the double gauge operators (analogous to \cite{Ans01}, \cite{Ejsmont1}) and compute the multidimensional moments of a joint distribution of Poisson operators. We show that the presented method of calculating negative arcs and restricted crossings is compatible with counting positive and negative inversions on a Coxeter group of type B. The present method is much simpler than using colored type-B set partitions in the sense of \cite{Ejsmont1}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Poisson Type Operators on the Double Fock Space of Type B Ejsmont, Wiktor Hęćka-Jędraszczyk, Patrycja Functional Analysis The double Fock space of type B was introduced in 2023 by Bożejko and Ejsmont (\cite{BE23}). In this article, we show the acting of Poisson type operators in that space. For this purpose, we define the double gauge operators (analogous to \cite{Ans01}, \cite{Ejsmont1}) and compute the multidimensional moments of a joint distribution of Poisson operators. We show that the presented method of calculating negative arcs and restricted crossings is compatible with counting positive and negative inversions on a Coxeter group of type B. The present method is much simpler than using colored type-B set partitions in the sense of \cite{Ejsmont1}. |
| title | The Poisson Type Operators on the Double Fock Space of Type B |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.10219 |