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.
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Doty, S., Giaquinto, A. Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2 . Algebras and Representation Theory 7, 1–17 (2004). https://doi.org/10.1023/B:ALGE.0000019386.04383.f9
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DOI: https://doi.org/10.1023/B:ALGE.0000019386.04383.f9