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Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2)

Stephen Doty·Anthony Giaquinto
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Abstract

We give a presentation of Schur algebras (over the rational number field) 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 Schur algebras, 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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BibTeXRIS

Stephen Doty, Anthony Giaquinto. 2000-10-01. Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2). https://arxiv.org/abs/math/0010005

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