q-Schur Algebras as Quotients of Quantized Enveloping Algebras Original Research Article

We study the properties of the surjective homomorphism, defined by Beilinson, Lusztig, and MacPherson, from the quantized enveloping algebra ofglnto theq-Schur algebra,Sq(n, r). In particular, we find an expression for the preimage of an arbitrary element ofSq(n, r) under this map and a basis for the kernel.