Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 040, 22 pages      arXiv:2202.13762
Contribution to the Special Issue on Non-Commutative Algebra, Probability and Analysis in Action

The Double Fock Space of Type B

Marek Bożejko a and Wiktor Ejsmont b
a) Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
b) Department of Telecommunications and Teleinformatics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Received March 28, 2022, in final form May 25, 2023; Published online June 12, 2023

In this article, we introduce the notion of a double Fock space of type B. We will show that this new construction is compatible with combinatorics of counting positive and negative inversions on a hyperoctahedral group.

Key words: Fock space; Coxeter arcsine distribution; Coxeter groups of type B; orthogonal polynomials.

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