Stephen Doty and Anthony Giaquinto
Presenting Schur algebras as quotients of the universal enveloping
algebra of $\mathfrak{gl}_2$

Abstract. We give a presentation of the Schur algebra $S_\mathbb Q(2,d)$
by generators and relations, in fact a presentation which is compatible
with Serre's presentation of the universal enveloping algebra of a simple
Lie algebra. In the process we find a new basis for $S_\mathbb Q(2,d)$, 
a truncated form of the usual PBW basis. We also locate the integral 
Schur algebra within the presented algebra as an analogue of Kostant's
$\mathbb Z$-form, and show that it has an integral basis which is a
truncated version of Kostant's basis.