TITLE: Meaning of fibration in Kazhdan and Lusztig's paper on affine flag manifolds
QUESTION [7 upvotes]: Kazhdan and Lusztig's paper "Fixed point varieties on affine flag manifolds" has the following definition on p.143: define inductively a variety $Z$ to be an "almost affine space" if $Z$ is affine or if there exists a fibration from $Z$ to an affine space such that all the fibers are "almost affine spaces" of smaller dimension. Also on p. 144 they construct various maps and claim them to be "algebraic fibrations". I am unsure what definition of fibration they are using, and am having difficulty inferring it from context.
Their maps they construct are surjective so it leads me to believe they might have meant "flat and surjective" but I am not sure since they never actually define "fibration" anywhere. 

Does anyone know precisely what they mean by "fibration"?

REPLY [5 votes]: According to Lusztig, it means locally trivial in the Zariski topology.