Azat M. Gainutdinov

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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 theW -algebra Wp,q that is the model symmetry (the maximal local algebra in the kernel), describe its(More)
We derive and study a quantum group gp,q that is Kazhdan–Lusztig-dual to the W -algebra Wp,q of the logarithmic (p, q) conformal field theory model. The algebra Wp,q is generated by two currentsW(z) andW(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 the quotient(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)
TheSL(2,Z)-representationπ on the center of the restricted quantum group Uqsl(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 Uqsl(2) ribbon element determines the decomposition of π into a(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)
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study(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)
For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is a root of unity (q = eiπ/p with integer p ≥ 2), the Bethe equations acquire continuous solutions, and the transfer(More)
The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N , we associate a pair of ‘divided polynomials’. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is(More)
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