The affine Temperley-Lieb algebras aTLN($beta$) are a family of infinite dimensional algebras generalizing the well-known Temperley-Lieb algebras TLN($beta$). They play, for the periodic XXZ chain, the role played by the original Temperley-Lieb algebra for the open XXZ chain. Their representation theory is much richer than that of the original TL family and admits a lot of similarities with the representation theory of the Virasoro algebra Vir. In particular, we will show in this talk that the representations of aTLN($beta$) on the periodic XXZ chains admits a structure akin that of the so-called Feigin-Fuchs Vir-modules. To do this, we will highlight the link between these representations and other canonical modules over aTLN($beta$) (the standard modules) while building up on the well-known quantum Schur-Weyl duality between TLN($beta$) and Uqsl2. The seminar is online only. Internet link to be collected from the Organizer:

Université de Laval (Canada)