Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl2 |
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Authors: | Stephen Doty Anthony Giaquinto |
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Institution: | (1) Mathematical and Computer Sciences, Loyola University Chicago, Chicago, Illinois, 60626, U.S.A. |
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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. |
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Keywords: | Schur algebra enveloping algebra generators and relations |
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