Marek Bożejko, Wiktor Ejsmont, “The Double Fock Space of Type B”, SIGMA, 2023, Volume 19,040, 22 pp.

The Double Fock Space of Type B

Marek Bożejko^a, 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

Abstract: 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.

Keywords: Fock space, Coxeter arcsine distribution, Coxeter groups of type B, orthogonal polynomials.

MSC: 6L53, 47N30, 46L54

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

Language: English

DOI: 10.3842/SIGMA.2023.040