under the baton of someone Definition

baton
noun

1. A light thin stick used by the conductor of an orchestra or choir, etc to direct them.
2. A short heavy stick carried by a policeman as a weapon. Also called truncheon. N Amer equivalent night stick.
3. A short stick passed from one runner to another in a relay race.
4. A stick carried, tossed and twirled, etc by a person at the head of a marching band.

Idiom: under the baton of someone

Said of a choir or orchestra, etc: conducted by them.

Etymology: 16c, meaning ‘a stick used as a weapon': from French bâton stick.

Info:

There is sometimes a spelling confusion between baton and batten.