Let Uq(Ĝ) denote the quantized affine Lie algebra and Uq(G (1)) the quantized nontwisted affine Lie algebra. Let Ofin be the category defined in section 3. We show that when the deformation parameter q is not a root of unit all integrable representations of Uq(Ĝ) in the category Ofin are completely reducible and that every integrable irreducible highest weight module over Uq(G (1)) correspondin...

We use the uniqueness of various invariant functionals on irreducible unitary representations of PGL2(R) in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new anisotropic analog. We deduce from these formulas non-trivial bounds for the corresponding unipotent and spherical Fourier coefficients of Maass forms. As an applicati...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary Coset Conformal Field Theories, i.e., gauged Wess-ZuminoWitten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic Quantum Field Theory (QFT) to approach Coset Conformal Field Theories. Two main conjectures are formulated and their consequences are discu...

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-ZuminoWitten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences are discussed. Some ...

Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM’s) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help o...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

A recent progress in a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS and Minkowski spaces is presented. The procedure is based on a BFV-BRST operator, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary irreducible representations of the AdS (Poincare) group. The constr...

The non-semisimple gl(2|2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(2|2) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten fr...