, Volume 7, Issue 1, pp 1-17

Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2

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Abstract

We give a presentation of the Schur algebras S 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 Q (2,d), a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis.