From additional symmetries to linearization of Virasoro symmetries

► The additional symmetries for the two-component BKP hierarchy are constructed. ► The Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy is obtained. ► Linearization of the Virasoro symmetries for the Drinfeld-Sokolov hierarchies of type D is proven. ► The Drinfeld-Sokolov and Dubrovin-Zhang integrable hierarchies of type D coincide. ► The topological solution of a D-type Drinfeld-Sokolov hierarchy admits the Virasoro constraints