Mathematics – Quantum Algebra
Scientific paper
2005-12-28
Theor.Math.Phys. 148 (2006) 1210-1235; Teor.Mat.Fiz. 148 (2006) 398-427
Mathematics
Quantum Algebra
31 pages, AMSLaTeX, xy, graphicx. V2: minor changes, references added
Scientific paper
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 C(p) of finite-dimensional representations of the restricted quantum group $U_q SL2$ at $q=e^{\frac{i\pi}{p}}$. 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 W(p)- and $U_q SL2$-representation categories is conjectured for all $p\ge 2$ and proved for p=2, the implications including the identifications of the quantum-group center with the logarithmic conformal field theory center and of the universal R-matrix with the braiding matrix.
Feigin BL
Gainutdinov AM
Semikhatov AM
Tipunin IYu
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