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Burau Representation of Braid Groups andq-Rationals

International Mathematics Research Notices
We establish a link between the new theory of q-deformed rational numbers and the classical Burau representation of the braid group B3. We apply this link to the open problem of classification of faithful complex specializations of this representation ...
Alexander Veselov, Valentin Ovsienko, Sophie Morier-Genoud   +2 more
exaly   +9 more sources

Weak faithfulness properties for the Burau representation [PDF]

Topology and Its Applications, 1996
We study the components of the matrices that belong to the image of the Burau representation of braids, and establish both algebraic and order constraints for a given Laurent polynomial to possibly be a component of such a Burau matrix. As an application
Patrick Dehornoy
exaly   +2 more sources

Burau representation and random walks on string links

Pacific Journal of Mathematics, 1998
This paper extensively revises the first author's preprint "Burau representation and random walks on knots". He would like to thank the warm hospitality of the math department of the Chinese University of Hong Kong where this revision was ...
Zhenghan Wang
exaly   +1 more source

Caractérisations de la représentation de Burau [PDF]

, 2003
This paper is devoted to characterizations of the (reduced) Burau representation of the Artin braid group, in terms of rigid local systems. We prove that the Burau representation is the only representation of the Hecke algebra for which some local system
Ivan Marin
exaly   +2 more sources

Tensor products of specializations of the Burau representation [PDF]

Journal of Pure and Applied Algebra, 2005
The reduced Burau representation is a one-parameter representation of Bn, the braid group on n strings. Specializing the parameter to a nonzero complex number y gives a representation βn(y):Bn→GL(Cn-1) which is either irreducible or has an irreducible ...
Mohammad N Abdulrahim, Edward Formanek
exaly   +2 more sources

On the irreducibility of the extensions of Burau and Gassner representations

Annali Dell'Universita Di Ferrara, 2021
Mohammad N Abdulrahim, Mohamad Nasser
exaly  

A categorification of the Burau representation at prime roots of unity

Selecta Mathematica, New Series, 2016
You Qi, Joshua Sussan
exaly  

Schur–Weyl-Type Duality for Quantized gl(1|1), the Burau Representation of Braid Groups, and Invariants of Tangled Graphs

Progress in Mathematics, 2012
Nicolai Reshetikhin, Ben Webster, Catharina Stroppel   +2 more
exaly  

The Burau representation is not faithful for n ≥ 6

Topology, 1993
D D Long
exaly