CIRM – Research in Pairs — The Virasoro Algebra as a Limit of Temperley-Lieb Algebras via Fusion Categories

The core problem of this project stems from the heuristic articulated by many authors in mathematics and mathematical physics over an extended period, (e.g. [1, 2, 6, 4], etc.) that when q 2 is a primitive ` th root of unity, there is a connection between limn→∞ TLn(q) where TLn(q) is the Temperley-Lieb algebra on the one hand, and the Virasoro algebra L = ⊕i∈ZCLi ⊕ CC on the other. The search for such a connection has hitherto led to many tantalising analogies, but as yet no definitive theorems.

We shall pursue two distinct approaches to the problem...