Representations of canonical anticommutation relations with orthogonality condition

Abstract

We study a class of *-representations of the *-algebra $$ A_0^{(d) } $$ generated by relations of the form $$ A_0^{(d) }=\mathbb{C}\langle{{a_j},a_j^{*}} |a_j^{*}{a_j}=1-{a_j}a_j^{*},a_i^{*}{a_j}=0,\;i\ne j,\;i\;j=1,\ldots,d\rangle $$ and propose a description of the classes of unitary equivalence of irreducible *-representations of $$ A_0^{(d) } $$ such that there exists j = 1, … , d for which $$a_j^{2}\ne 0 $$ .