The University of Southampton
University of Southampton Institutional Repository

The explicit construction of irreducible representations of the quantum algebras U_q(sl(n))

Burdik, C., King, R.C. and Welsh, T.A. (2001) The explicit construction of irreducible representations of the quantum algebras U_q(sl(n)) In, New Developments in Fundamental Interaction Theories: 37th Karpacz Winter School of Theoretical Physics. 37th Karpacz Winter School of Theoretical Physics New York, USA, American Institute of Physics pp. 158-169. (AIP Conference Proceedings, 589). (doi:10.1063/1.1419323).

Record type: Book Section


The duality between the quantum algebra Uq(sl(n)) and the Hecke algebra Hm(q2) first pointed out by Jimbo is exploited to construct explicit irreducible representations of Uq(sl(n)). The method is based on the use of Young tableaux and involves the notion of q-dependent Young symmetrisers. A key role is played by q-dependent generalisations of the Garnir identities. The appropriate algorithm is first described and illustrated in the generic case for which q is not a root of unity. All matrix elements for the irreducible representations of Uq(sl(3)) are given. The complications that arise in the non-generic case for which q is a primitive p-th root of unity are then addressed. Explicit results on both irreducible and indecomposable representations are presented.

Full text not available from this repository.

More information

Published date: 2001
Venue - Dates: 37th Karpacz Winter School of Theoretical Physics, 2001-02-06 - 2001-02-15


Local EPrints ID: 29528
ISBN: 0735400296
PURE UUID: da2460f3-3f40-4e2c-97db-ad689a587cfe

Catalogue record

Date deposited: 12 May 2006
Last modified: 17 Jul 2017 15:57

Export record



Author: C. Burdik
Author: R.C. King
Author: T.A. Welsh

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.