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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeOct 19th 2019
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added few references, e.g. on the logarithmic CFT case. Maybe the entry should be fused with [[fusion ring]], I see no reason to discuss it separately, the entries are both sketchy and have little material so far. <a href="https://ncatlab.org/nlab/revision/diff/Verlinde+formula/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/Verlinde+formula/4">v4</a>, <a href="https://ncatlab.org/nlab/show/Verlinde+formula">current</a>

   I added few references, e.g. on the logarithmic CFT case. Maybe the entry should be fused with fusion ring, I see no reason to discuss it separately, the entries are both sketchy and have little material so far.

   diff, v4, current

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeOct 19th 2019
   • PermaLink
   Author: zskoda
   Format: MarkdownItexSorry, I meant [[Verlinde ring]] entry.

   Sorry, I meant Verlinde ring entry.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the following to the References-section: *** Original article: * [[Erik Verlinde]], *Fusion rules and modular transformations in 2D conformal field theory*, Nuclear Physics B **300** (1988) 360-376 $[$<a href="https://doi.org/10.1016/0550-3213(88)90603-7">doi:10.1016/0550-3213(88)90603-7</a>$]$ Proofs of the Verlinde formula: * {#TUY89} A. Tsuchiya, [[Kenji Ueno]], and Y. Yamada, *Conformal field theory on the universal family of stable curves with gauge symmetry* In: *Conformal field theory and solvable lattice models* Adv. Stud. Pure Math. **16** (1989), 297–372. * {#Faltings94} [[Gerd Faltings]], *A proof for the Verlinde formula*, J. Alg. Geom. **3** (1994) 347–374 * {#Huang} [[Yi-Zhi Huang]], *Vertex operator algebras, the Verlinde conjecture and modular tensor categories*, Proc. Nat. Acad. Sci. **102** (2005) 5352-5356 $[$[arXiv:math/0412261](http://arxiv.org/abs/math/0412261), [doi:10.1073/pnas.0409901102](https://doi.org/10.1073/pnas.0409901102)$]$ Review in: * [[Martin Schottenloher]], *Mathematical Aspects of the Verlinde Formula*, in: *A Mathematical Introduction to Conformal Field Theory*, Lecture Notes in Physics **759**, Springer (2008) $[$[doi:10.1007/978-3-540-68628-6](https://link.springer.com/book/10.1007/978-3-540-68628-6), [web](https://www.mathematik.uni-muenchen.de/~schotten/LNP-cft-pdf/), [pdf](https://www.mathematik.uni-muenchen.de/~schotten/LNP-cft-pdf/11_978-3-540-68625-5_Ch11_23-08-08.pdf)$]$ where it says (p. 213): > Several mathematicians have worked on the problem of proving the Verlinde formula, starting with $[$[TUY89](#TUY89)$]$ and coming to a certain end with $[$[Fal94](#Faltings94)$]$. These proofs are all quite difficult to understand. *** <a href="https://ncatlab.org/nlab/revision/diff/Verlinde+formula/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Verlinde+formula/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Verlinde+formula">current</a>

   added the following to the References-section:

   ---

   Original article:

   • Erik Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nuclear Physics B 300 (1988) 360-376 $[$doi:10.1016/0550-3213(88)90603-7$]$

   Proofs of the Verlinde formula:

   • {#TUY89} A. Tsuchiya, Kenji Ueno, and Y. Yamada, Conformal field theory on the universal family of stable curves with gauge symmetry In: Conformal field theory and solvable lattice models Adv. Stud. Pure Math. 16 (1989), 297–372.

   • {#Faltings94} Gerd Faltings, A proof for the Verlinde formula, J. Alg. Geom. 3 (1994) 347–374

   • {#Huang} Yi-Zhi Huang, Vertex operator algebras, the Verlinde conjecture and modular tensor categories, Proc. Nat. Acad. Sci. 102 (2005) 5352-5356 $[$arXiv:math/0412261, doi:10.1073/pnas.0409901102$]$

   Review in:

   • Martin Schottenloher, Mathematical Aspects of the Verlinde Formula, in: A Mathematical Introduction to Conformal Field Theory, Lecture Notes in Physics 759, Springer (2008) $[$doi:10.1007/978-3-540-68628-6, web, pdf$]$

   where it says (p. 213):

   Several mathematicians have worked on the problem of proving the Verlinde formula, starting with $[$TUY89$]$ and coming to a certain end with $[$Fal94$]$. These proofs are all quite difficult to understand.

   ---

   diff, v6, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 17th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Ralph Blumenhagen]], [[Erik Plauschinn]], §4.3 of: *Introduction to Conformal Field Theory -- With Applications to String Theory*, Lecture Notes in Physics **779**, Springer (2009) &lbrack;[doi:10.1007/978-3-642-00450-6](https://doi.org/10.1007/978-3-642-00450-6)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Verlinde+formula/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/Verlinde+formula/7">v7</a>, <a href="https://ncatlab.org/nlab/show/Verlinde+formula">current</a>

   added pointer to:

   • Ralph Blumenhagen, Erik Plauschinn, §4.3 of: Introduction to Conformal Field Theory – With Applications to String Theory, Lecture Notes in Physics 779, Springer (2009) [doi:10.1007/978-3-642-00450-6]

   diff, v7, current