Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center

By B. Feigin, A. Gainutdinov, A. M. Semikhatov, I. Tipunin. 2005

219 citations recorded by the source corpus.

The SL(2, ℤ)-representation π on the center of the restricted quantum group at the primitive 2pth 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 ribbon element determines the decomposition of π 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 at the primitive 2pth 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 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b895d6df9f63cbf4496c5196d00aa6c9451e6876

How researchers see this paper

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In Algebra and Number Theory

1. A. Gainutdinov
2. I. Tipunin
3. A. M. Semikhatov
4. B. Feigin
5. David Ridout
6. T. Creutzig

In Geometry and Topology

1. T. Creutzig
2. David Ridout
3. A. Gainutdinov
4. B. Feigin
5. I. Tipunin
6. A. M. Semikhatov

In Mathematical Physics

1. T. Creutzig
2. David Ridout
3. A. Gainutdinov
4. B. Feigin
5. I. Tipunin
6. A. M. Semikhatov

Citations in the corpus

• Logarithmic extensions of minimal models: characters and modular transformations. (2006, methodology): “A number of result s exist on the (p,1) models [19, 20, 21, 22 ], but no model has been investigated so completely as the Ising model, for example.”
• Logarithmic conformal field theory: beyond an introduction (2013, background): “The singlet, being a subalgebra of the triplet, has received relatively little attention, but the W ( 1, p ) -models have been considered by a variety of groups [38, 104–109].”