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Study of Gram matrices in Fock representation of multiparametric canonical commutation relations, extended Zagier's conjecture, hyperplane arrangements and quantum groups

Department of Mathematics, University of Osijek
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  • Multiparametric Canonical Commutation Relations
  • Deformed Partial Derivatives
  • Lattice Of Subdivisions
  • Deformed Regular Representation
  • Quantum Bilinear Form
  • Zagier'S Conjecture
  • Mathematics


In this Colloquium Lecture D.Svrtan reported on the joined research with S.Meljanac on the subject given in the title. By quite laborious mathematics it is explained how one can handle systems in which each Heisenberg commutation relation is deformed separately. For Hilbert space realizability a detailed determinant computations (extending Zagier's one - parametric formulas) are carried out. The inversion problem of the associated Gram matrices on Fock weight spaces is completely solved (Extended Zagier's conjecture) and a counterexample to the original Zagier's conjecture is presented in detail.

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