On Schur algebras and little Schur algebras

Let ζr be the natural algebra homomorphism from the enveloping algebra UQ(η) of glη to the Schur algebra SQ(η,r). We will present a BLM-realization of UQ(η) and the restricted enveloping algebra of glη. This result will be used to construct various bases for UQ(η,r):=ζr(UQ(η)) and little Schur algebras. Finally we will discuss the relation between the little q-Schur algebra and the little Schur algebra through the construction of a B-basis for the little q-Schur algebra over B. Here B=Z[ε,ε−1] and ε∈C is an lth primitive root of 1 with l⩾3 being odd.