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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
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
¯\EuScriptUqsℓ(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
¯\EuScriptUqsℓ(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
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
Linking options:
https://www.mathnet.ru/eng/tmf2324https://doi.org/10.4213/tmf2324 https://www.mathnet.ru/eng/tmf/v148/i3/p398
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