On Krammer's Representation of the Braid Group
Matthew G. Zinno
Abstract
A connection is made between the Krammer representation and the Birman-Murakami-Wenzl algebra. Inspired by a dimension argument, a basis is found for a certain irrep of the algebra, and relations which generate the matrices are found. Following a rescaling and change of parameters, the matrices are found to be identical to those of the Krammer representation. The two representations are thus the same, proving the irreducibility of one and the faithfulness of the other.
Create a lesson
Related papers
Higher mod p Satake transforms: explicit formulas and images for GL2
Hargun Bhatia, Yashi Jain, Casey Perdue et al.
Lusztig Parameters and Factorizations of Determinantial Modules
Yingjin Bi
Twisted Jacquet modules and induction from Speh representations
Alan Xuelun Hou
Sharp commutator bounds on complex simple Lie algebras: the Böttcher--Wenzel inequality and the comass of the Cartan 3-form
Daniel J. F. Fox
Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers
Tianle Liu
Reciprocity for projective and injective direct summands
Shigeo Koshitani, Taro Sakurai