The Interplay between Linear Representations of the Braid Group
2007 ◽
Vol 2007
◽
pp. 1-9
Keyword(s):
We consider Wada's representation as a twisted version of the standard action of the braid group,Bn, on the free group withngenerators. Constructing a free group,Gnm, of ranknm, we compose Cohen's mapBn→Bnmand the embeddingBnm→Aut(Gnm)via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation andm−1copies of the standard representation after changing the parameterttotkin the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.
2003 ◽
Vol 02
(02)
◽
pp. 169-175
◽
2005 ◽
Vol 14
(08)
◽
pp. 1087-1098
◽
Keyword(s):
2015 ◽
Vol 24
(12)
◽
pp. 1550065
Keyword(s):
1993 ◽
Vol 02
(04)
◽
pp. 399-412
◽
Keyword(s):
1991 ◽
Vol 110
(2)
◽
pp. 225-228
Keyword(s):
2020 ◽
Vol 29
(01)
◽
pp. 1950097
Keyword(s):
2017 ◽
Vol 164
(3)
◽
pp. 493-530
◽
2018 ◽
Vol 1116
◽
pp. 022034