Fock space associated to Coxeter group of type B
Marek Bo\.zejko, Wiktor Ejsmont, Takahiro Hasebe

TL;DR
This paper constructs a generalized Gaussian process linked to Coxeter groups of type B using an $(eta,q)$-Fock space, deriving new commutation relations, norm estimates, and connections to orthogonal polynomials like $q$-Meixner-Pollaczek.
Contribution
It introduces a novel $(eta,q)$-Fock space framework with specific commutation relations and explores its probabilistic and polynomial structures, extending previous models.
Findings
Derived a new commutation relation for creation and annihilation operators.
Established the distribution of certain operators as a generalized Gaussian.
Connected the distribution to $q$-Meixner-Pollaczek and related orthogonal polynomials.
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 -Fock space, which satisfy the commutation relation where are elements of a complex Hilbert space with a self-adjoint involution and is the number operator with respect to the grading on the -Fock space. We give an estimate of the norms of creation operators. We show that the distribution of the operators 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…
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