Mr Dimitris Michailidis (University of Kent) gives a maths seminar at the School of Mathematics, UEA. The talk is on “On bases and BGG resolutions of Temperley-Lieb algebras of type B”. The abstract is below.

Inspired from the study of certain models in physics, Martin and Saleur defined the Temperley-Lieb algebra of type B or blob algebra as the diagrammatic two parameter generalisation of the Temperley-Lieb algebra of type A. The blob algebra can also be viewed as quotient of the Hecke algebra of type B, hence it is isomorphic to a quotient of the (graded) KLR algebra via the Brundan-Kleshchev isomorphism. In this talk we shall construct bases of the simple representations for the blob algebra, indexed by paths in the Euclidean space with respect to the alcove geometry of affine type A1. We also prove that to each simple representation we attach a resolution of cell modules, called BGG resolution, which gives homological construction of simple representations.