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We study logarithmic conformal field models that extend the (p, q) Virasoro minimal models. For coprime positive integers p and q, the model is defined as the kernel of the two minimal-model screening operators. We identify the field content, construct the W-algebra W p,q that is the model symmetry (the maximal local algebra in the kernel), describe its(More)
The SL(2, Z)-representation π on the center of the restricted quantum group U q sℓ(2) at the primitive 2pth root of unity is shown to be equivalent to the SL(2, Z)-representation on the extended characters of the logarithmic (1, p) conformal field theory model. The Jordan decomposition of the U q sℓ(2) ribbon element determines the decomposition of π into a(More)
We derive and study a quantum group g p,q that is Kazhdan–Lusztig-dual to the W-algebra W p,q of the logarithmic (p, q) conformal field theory model. The algebra W p,q is generated by two currents W + (z) and W − (z) of dimension (2p−1)(2q−1), and the energy–momentum tensor T (z). The two currents generate a vertex-operator ideal R with the property that(More)
Nontrivial critical models in 2D with a central charge c=0 are described by logarithmic conformal field theories (LCFTs), and exhibit, in particular, mixing of the stress-energy tensor with a "logarithmic" partner under a conformal transformation. This mixing is quantified by a parameter (usually denoted b), introduced in Gurarie [Nucl. Phys. B546, 765(More)
We introduce a Kazhdan–Lusztig-dual quantum group for (1, p) Virasoro logarithmic minimal models as the Lusztig limit of the quantum sℓ(2) at p th root of unity and show that this limit is a Hopf algebra. We calculate tensor products of irreducible and projective representations of the quantum group and show that these tensor products coincide with the(More)
We introduce p − 1 pseudocharacters in the space of (1, p) model vacuum torus amplitudes to complete the distinguished basis in the 2p-dimensional fusion algebra to a basis in the whole (3p − 1)-dimensional space of torus amplitudes, and the structure constants in this basis are integer numbers. We obtain a generalized Verlinde-formula that gives these(More)
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