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Fock space associated to Coxeter groups of type B
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| Title: | Fock space associated to Coxeter groups of type B |
| Authors: | Bożejko, Marek Browse this author | | Ejsmont, Wiktor Browse this author | | Hasebe, Takahiro Browse this author →KAKEN DB |
| Keywords: | Noncommutative probability | | q-Gaussian process | | Fock spaces |
| Issue Date: | 15-Sep-2015 |
| Journal Title: | Journal of Functional Analysis |
| Volume: | 269 |
| Issue: | 6 |
| Start Page: | 1769 |
| End Page: | 1795 |
| Publisher DOI: | 10.1016/j.jfa.2015.06.026 |
| Abstract: | In this article we construct a generalized Gaussian process coming from Coxeter groups of type B. It is given by creation and annihilation operators on an (α,q)-Fock space, which satisfy the commutation relation
$b_{α,q}(x)b^∗_{α,q}(y)−qb^∗_{α,q}(y)b_{α,q}(x)=⟨x,y⟩I+α⟨\overline{x},y⟩q^{2N}$,
where x,y are elements of a complex Hilbert space with a self-adjoint involution $x↦\overline{x}$ and N is the number operator with respect to the grading on the (α,q)-Fock space. We give an estimate of the norms of creation operators. We show that the distribution of the operators $b_{α,q}(x)+b^∗_{α,q}(x)$ with respect to the vacuum expectation becomes a generalized Gaussian distribution, in the sense that all mixed moments can be calculated from the second moments with the help of a combinatorial formula related with set partitions. Our generalized Gaussian distribution associates the orthogonal polynomials called the q-Meixner-Pollaczek polynomials, yielding the q-Hermite polynomials when α=0 and free Meixner polynomials when q=0. |
| Rights: | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76025 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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