Determinants and Inversion of Gram Matrices in Fock Representation of $\{q_{kl}\}$- Canonical Commutation Relations and Applications to Hyperplane Arrangements and Quantum Groups. Proof of an Extension of Zagier's Conjecture

Stjepan Meljanac, Dragutin Svrtan

In this paper we study a collections of operators $a(k)$ satisfying the "$q_{kl}$-canonical commutation relations" $a(k)a^{+}(l)-q_{kl}{a}^{+}(l)a(k)={\delta }_{kl}$ (corresponding for $q…