Dispersionless bigraded Toda Hierarchy and its additional symmetry

In this paper, we firstly give the definition of dipersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov-Schulman’s ${\text{M}}_L$, ${\text{M}}_R$ operator and give the additional Block symmetry of dBTH. Meanwhile we give tau function of dBTH and some some related dipersionless bilinear equations.