Abstract
The Schur algebras are realized in the ring of constructible functions on the generalized Steinberg varieties attached to the n -step flag varieties. The semicanonical bases for Schur algebras are defined and shown to behave in the simplest possible way under the transfer maps. Such a property of the semicanonical basis is conjectured in Lusztig (2002) [L6, 5.5] .
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