Presenting Schur Algebras as Quotients of the Universal Enveloping Algebra of gl_{2}

Authors

Stephen Doty

Mathematical and Computer SciencesLoyola University Chicago

Anthony Giaquinto

Mathematical and Computer SciencesLoyola University Chicago

Article

DOI:
10.1023/B:ALGE.0000019386.04383.f9

Cite this article as:

Doty, S. & Giaquinto, A. Algebras and Representation Theory (2004) 7: 1. doi:10.1023/B:ALGE.0000019386.04383.f9

34Views

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.

Schur algebraenveloping algebragenerators and relations