Gandalf (Pure Maths Student Seminar): Skew Howe duality in Type A quantum knot invariants
4 November 2015 16:00 in CM221
Both the Jones polynomial and the Alexander polynomial can be viewed as invariants arising from the representations of quantum (super)groups in type A. Skew Howe duality give these invariants particularly nice descriptions in terms of trivalent diagrams. This method is particularly powerful when defining knot homology theories categorifying these polynomials. I will discuss the relationship between representations of quantum groups and the trivalent diagrams appearing in calculations of knot invariants, and describe how this can be used to understand knot homology theories, and progress towards obtaining a 'quantum' categorification of the Alexander polynomial.
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.