Virasoro algebra in $K$-space

We introduce a novel representation of Virasoro algebra in open string field theory. Elements of the algebra are vector fields on the $K$-space, where $K$ is the string field that generates a world sheet strip in sliver frame. The generators introduce a global symmetry of open string field theory. We also derive a representation of Virasoro algebra for nontrivial open string background described by the formal pure gauge solution. Generators for 0, 1 and 2 D-branes are explicitly studied and different behaviors around $K=0$ are observed.