Categorification of the Kazhdan-Lusztig basis of the Temperley-Lieb algebra by bimodules

Thomas Gobet (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We realize the Temperley-Lieb algebra by analogues of Soergel bimodules. The key point is that the monoidal structure is not given by a usual tensor product but by a slightly more complicated operation.

Mots clés: Temperley-Lieb algebras; Soergel bimodules; categorification

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

Thomas Gobet. Categorification of the Kazhdan-Lusztig basis of the Temperley-Lieb algebra by bimodules. 2012. ⟨hal-00763307v2⟩