## Fock space associated to Coxeter groups of type B

### Marek Bożejko , Wiktor Ejsmont , Takahiro Hasebe

#### 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)(α,q)-Fock space, which satisfy the commutation relation View the MathML sourcebα,q(x)bα,q⁎(y)−qbα,q⁎(y)bα,q(x)=〈x,y〉I+α〈x‾,y〉q2N, where x,yx,y are elements of a complex Hilbert space with a self-adjoint involution View the MathML sourcex↦x¯ and N is the number operator with respect to the grading on the (α,q)(α,q)-Fock space. We give an estimate of the norms of creation operators. We show that the distribution of the operators View the MathML sourcebα,q(x)+bα,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 is associated to the orthogonal polynomials called the q-Meixner–Pollaczek polynomials, yielding the q -Hermite polynomials when α=0α=0 and free Meixner polynomials when q=0q=0.Author | |||||

Journal series | Journal of Functional Analysis, ISSN 0022-1236, (A 40 pkt) | ||||

Issue year | 2015 | ||||

Vol | 269 | ||||

No | 6 | ||||

Pages | 1769-1795 | ||||

Publication size in sheets | 1.3 | ||||

Keywords in English | Noncommutative probability; q-Gaussian process; Fock spaces | ||||

DOI | DOI:10.1016/j.jfa.2015.06.026 | ||||

URL | http://www.sciencedirect.com/science/journal/00221236/269/6?sdc=1 | ||||

Language | en angielski | ||||

File |
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Score (nominal) | 40 | ||||

Citation count* |

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.

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