Braid group approach to the derivation of universal Ř matrices

Abstract

A new method for deriving universal Ř matrices from braid group representation is discussed. In this case, universal Ř operators can be defined and expressed in terms of products of braid group generators. The advantage of this method is that matrix elements of Ř are rank independent, and leaves multiplicity problem concerning coproducts of the corresponding quantum groups untouched. As examples, Ř matrix elements of $[1]\times [1]$, $[2]\times [2]$, $[1^2]\times [1^2]$, and $[21]\times [21]$ with multiplicity two for $A_n$, and $[1]\times [1]$ for $B_n$, $C_n$, and $D_n$ type quantum groups, which are related to Hecke algebra and Birman-Wenzl algebra, respectively, are derived by using this method.

20 pages, LaTeX