Fock spaces associated with Coxeter groups of type B
Apparaît dans la collection : Combinatorics and Arithmetic for Physics: special days 2023
In the talk we give the construction of Fock space related to the infinite hyperoctahedral group,which is related to the two-parameters function $F(q_+, q_−)$. We show that $F(q_+, q_−)$. is positive definite if and only if it is an extreme character of the infinite hyperoctahedral group and we classify the corresponding set of parameters $q_+$ and $q_−$. We apply our construction to a cyclic Fock space of type B, generalizing the results of Bozejko and Guta.
