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]×[1]
,
[2]×[2]
,
[
1
2
]×[
1
2
]
, and
[21]×[21]
with multiplicity two for
A
n
, and
[1]×[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.