SPEAKER:
Azat Gaynutdinov (CEA Saclay)

TITLE:
From Temperley-Lieb algebras to representations of Virasoro algebras: modules, fusion, and operator algebras

ABSTRACT:
We study tensor-product representations of Temperley-Lieb (TL) algebras (quantum spin-chains) and the associated "fusion" of TL modules at roots of unity case. Using quantum group results, we provide rigorous calculations of the fusion of various TL modules. Our results are illustrated by many explicit examples relevant for physics. On the level of operator algebras, an analogue of the Howe duality in such systems allowed to take an inductive limit of these spin-chains when the number of tensorands (sites) goes to infinity. The limit of the TL representation spaces turns out to be a logarithmic conformal field theory, while the TL algebra in the inductive limit is expressed by a Virasoro algebra representation. We discuss how indecomposability arises in the TL fusion and compare the mechanisms involved with similar observations in the corresponding conformal field theory.