LAUSR

In the work of Doty and Giaquinto [Int. Math. Res. Not. 36, 1907 (2002)] and Du and Parshall [Trans. Am. Math. Soc. 355, 1593 (2003)], the presentations of q-Schur algebra as a quotient of quantum gln are given. Doty and Giaquinto [Electron. Res. Announce. Am. Math. Soc. 7, 54 (2001)] obtained the presentation for the Schur algebra U(2, r) and q-Schur algebra U(2, r) as a quotient of classical, quantized enveloping algebra of sl2, respectively. They pointed out that the problem of presenting q-Schur algebra U(n, r) as a quotient of quantized enveloping algebra of sln seems to be more difficult for n > 2. Inspired by this point of view, we obtain a presentation for the Schur algebra, both the classical and quantized case, as a quotient of classical, quantized enveloping algebra of sln, respectively, in this paper.In the work of Doty and Giaquinto [Int. Math. Res. Not. 36, 1907 (2002)] and Du and Parshall [Trans. Am. Math. Soc. 355, 1593 (2003)], the presentations of q-Schur algebra as a quotient of quantum gln are given. Doty and Giaquinto [Electron. Res. Announce. Am. Math. Soc. 7, 54 (2001)] obtained the presentation for the Schur algebra U(2, r) and q-Schur algebra U(2, r) as a quotient of classical, quantized enveloping algebra of sl2, respectively. They pointed out that the problem of presenting q-Schur algebra U(n, r) as a quotient of quantized enveloping algebra of sln seems to be more difficult for n > 2. Inspired by this point of view, we obtain a presentation for the Schur algebra, both the classical and quantized case, as a quotient of classical, quantized enveloping algebra of sln, respectively, in this paper.