  In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then
use them to construct the additional symmetries of the bigraded Toda hierarchy
(BTH). We further show that these additional symmetries form an interesting
infinite dimensional Lie algebra known as a Block type Lie algebra, whose
structure theory and representation theory have recently received much
attention in literature. By acting on two different spaces under the weak
W-constraints we find in particular two representations of this Block type Lie
algebra.
