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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 148, Number 3, Pages 398–427
DOI: https://doi.org/10.4213/tmf2324
(Mi tmf2324)
 

This article is cited in 114 scientific papers (total in 114 papers)

Kazhdan–Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT

A. M. Gainutdinova, A. M. Semikhatovb, I. Yu. Tipuninb, B. L. Feiginc

a M. V. Lomonosov Moscow State University, Faculty of Physics
b P. N. Lebedev Physical Institute, Russian Academy of Sciences
c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
References:
Abstract: To study the representation category of the triplet W-algebra W(p) that is the symmetry of the (1,p) logarithmic conformal field theory model, we propose the equivalent category \EuScriptCp of finite-dimensional representations of the restricted quantum group ¯\EuScriptUqs(2) at q=eiπ/p. We fully describe the category \EuScriptCp 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 W(p)- and ¯\EuScriptUqs(2)-representation categories is conjectured for all p 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.
Keywords: Kazhdan–Lusztig correspondence, quantum groups, logarithmic conformal field theories, indecomposable representations.
Received: 31.12.2005
English version:
Theoretical and Mathematical Physics, 2006, Volume 148, Issue 3, Pages 1210–1235
DOI: https://doi.org/10.1007/s11232-006-0113-6
Bibliographic databases:
Language: Russian
Citation: A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin, B. L. Feigin, “Kazhdan–Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT”, TMF, 148:3 (2006), 398–427; Theoret. and Math. Phys., 148:3 (2006), 1210–1235
Citation in format AMSBIB
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