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The Erwin Schroedinger Institute for Mathematical Physics

Daniel Tubbenhauer (U Louvain): From Dualities to Diagrams

 

Abstract:

The Temperley-Lieb algebra T Ld has its origin in the study of sl2-modules: Rumer, Teller and Weyl showed (more or less) already in the 30ties that T Ld can be seen as a diagrammatic realization of the representation category of sl2-modules - providing a topological (and fun!) tool to study the latter.

In this talk I try to explain how one can proof such a realization. Our main tool is “a machine that takes dualities and produces diagrammatic categories”. In particular, we show explicitly how this “machine” works if one feeds it with q-Howe duality – which produces diagrammatic presentations of categories of sln-modules akin to the Temperley-Lieb calculus.

As an application, I give a diagrammatic version of a symmetry of HOMFLY-PT polynomials.

In principal, everything in this talk is amenable to categorification, but we have to stay in the uncategorified world for the moment.

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At a glance

Type: Lecture
When: May 13, 2015
from 02:00 PM to 03:00 PM
Where: ESI, Schrödinger Lecture Hall
Organizers: Nils Carqueville (ESI, U Vienna)
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