Schur-Weyl type duality for quantized gl(1|1),the Burau representation of braid groups and invariants of tangled graphs

Abstract

We show that the Schur-Weyl type duality between $gl(1|1)$ and $G{L}_n$ gives a natural representation-theoretic setting for the relation between reduced and non-reduced Burau representations.

12 pages. The paper was written in 2010 and published in: Perspectives in analysis, geometry, and topology : On the occasion of the 60th birthday of Oleg Viro; Edi- tors: Ilia Itenberg, Burglind Joricke, Mikael Passare, Birkhauser Verlag GmbH, 2012