Abstract
A variation of the ZamolodchikovâFaddeev algebra over a finite-dimensional Hilbert space {mathcal {H}} and an involutive unitary R-Matrix S is studied. This algebra carries a natural vacuum state, and the corresponding Fock representation spaces {mathcal {F}}_S({mathcal {H}}) are shown to satisfy {mathcal {F}}_{Sboxplus R}({{mathcal {H}}}oplus {{mathcal {K}}}) cong {mathcal {F}}_S({{mathcal {H}}})otimes {mathcal {F}}_R({{mathcal {K}}}), where Sboxplus R is the box-sum of S (on {{mathcal {H}}}otimes {{mathcal {H}}}) and R (on {{mathcal {K}}}otimes {{mathcal {K}}}). This analysis generalises the well-known structure of Bose/Fermi Fock spaces and a recent result of Pennig. These representations are motivated from quantum field theory (short-distance scaling limits of integrable models).
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