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

by Doty, Stephen; Giaquinto, Anthony

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.

DOI: 10.1023/B:ALGE.0000019386.04383.f9
Print publication date: 3/1/2004
View article on SpringerLink

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