Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-11
Commun.Math.Phys. 265 (2006) 47-93
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, amsart++, xy, 51 pages. V3: minor changes, some factors of $i$ sorted out, a reference added. V4: the very final versio
Scientific paper
10.1007/s00220-006-1551-6
The SL(2,Z) representation $\pi$ on the center of the restricted quantum group U_{q}sl(2) at the primitive 2p-th 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 multiplicative Jordan decomposition of the U_{q}sl(2) ribbon element determines the decomposition of $\pi$ into a ``pointwise'' product of two commuting SL(2,Z) representations, one of which restricts to the Grothendieck ring; this restriction is equivalent to the SL(2,Z) representation on the (1,p)-characters, related to the fusion algebra via a nonsemisimple Verlinde formula. The Grothendieck ring of U_{q}sl(2) at the primitive 2p-th root of unity is shown to coincide with the fusion algebra of the (1,p) logarithmic conformal field theory model. As a by-product, we derive q-binomial identities implied by the fusion algebra realized in the center of~U_{q}sl(2).
Feigin BL
Gainutdinov AM
Semikhatov AM
Tipunin IYu
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