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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
22 pages; submitted to Algebras and Representation Theory

Keywords

Representation Theory, Rings and Algebras, 16S30; 16P10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/60022

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0010005
 http://arxiv.org/abs/math/0010005

Collections

arXiv