  In 1996, Tong, Yang and Ma defined a family of representations of the braid
group which have the same dimensions as the (unreduced) Burau representations
but are not equivalent. The Burau representation was defined homologically and
extended to the string links in several ways. In this paper, using the method
of Silver and Williams, we extend the family of the Tong-Yang-Ma
representations to the string links and welded string links. Moreover, we show
that the kernels of these representations may be described using some linking
numbers. Finally, we apply the Long-Moody construction to the Tong-Yang-Ma
representations and study its first properties.
