caa a22 4500 467910847 CHVBK 20180406152848.0 cr unu---uuuuu 170328e20060901xx s 000 0 eng 10.1007/s11232-006-0113-6 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0113-6 Kazhdan-Lusztig correspondence for the representation category of the triplet W -algebra in logarithmic CFT [Elektronische Daten] [A. Gainutdinov, A. Semikhatov, I. Tipunin, B. Feigin] To study the representation category of the triplet W-algebra $$\mathcal{W}\left( p \right)$$ that is the symmetry of the (1, p) logarithmic conformal field theory model, we propose the equivalent category C p of finite-dimensional representations of the restricted quantum group Ū q sℓ(2) at $$\mathfrak{q} = e^{{{i\pi } \mathord{\left/ {\vphantom {{i\pi } p}} \right. \kern-\nulldelimiterspace} p}} $$ . We fully describe the category C p by classifying all indecomposable representations. These are exhausted by projective modules and three series of representations that are essentially described by indecomposable representations of the Kronecker quiver. The equivalence of the $$\mathcal{W}\left( p \right)$$ -and Ū q sℓ(2)-representation categories is conjectured for all p = 2 and proved for p = 2. The implications include identifying the quantum group center with the logarithmic conformal field theory center and the universal R-matrix with the braiding matrix. Springer Science+Business Media, Inc., 2006 Kazhdan-Lusztig correspondence nationallicence quantum groups nationallicence logarithmic conformal field theories nationallicence indecomposable representations nationallicence Gainutdinov A. Physics Department, Moscow State University, Moscow, Russia aut Semikhatov A. Lebedev Physical Institute, RAS, Moscow, Russia aut Tipunin I. Lebedev Physical Institute, RAS, Moscow, Russia aut Feigin B. Landau Institute for Theoretical Physics, RAS, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/3(2006-09-01), 1210-1235 0040-5779 148:3<1210 2006 148 11232 https://doi.org/10.1007/s11232-006-0113-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0113-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gainutdinov A. Physics Department, Moscow State University, Moscow, Russia aut NATIONALLICENCE 700 1- Semikhatov A. Lebedev Physical Institute, RAS, Moscow, Russia aut NATIONALLICENCE 700 1- Tipunin I. Lebedev Physical Institute, RAS, Moscow, Russia aut NATIONALLICENCE 700 1- Feigin B. Landau Institute for Theoretical Physics, RAS, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/3(2006-09-01), 1210-1235 0040-5779 148:3<1210 2006 148 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer