Pure Maths Colloquium: Diagram algebras and affine tangles
31 October 2011 16:00 in CM221
Many diagram algebras have originated from a vast range of areas in mathematics and physics; for example, the Temperley-Lieb algebras from statistical mechanics, the Brauer algebras from the study of the representation theory of orthogonal and symplectic groups, and the Birman-Murakami-Wenzl (BMW) algebras from the Kauffman link invariant and knot theory. They share a close relationship with each other, and are also connected to the Artin braid group of type A, Lawrence-Krammer representations and Iwahori-Hecke algebras of the symmetric group.
In view of these relationships between the BMW, Brauer and Temperley-Lieb algebras and several objects of "type A", various authors have since naturally generalized them for other types of Artin groups and complex reflection groups. The aim of this talk is to discuss the cyclotomic BMW algebras, which were introduced by Haering-Oldenburg and inspired by the cyclotomic Hecke algebras of type G(k,1,n) (aka Ariki-Koike algebras) and type B knot theory. We give a diagrammatic realization of this algebra in terms of affine/cylindrical tangles and discuss its cellular structure, in the sense of Graham and Lehrer.
NO in-depth knowledge of knot theory or familiarity with these algebras is required for this talk.
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