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

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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.

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Citation

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).

More information

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

Identifiers

Local EPrints ID: 29528
URI: http://eprints.soton.ac.uk/id/eprint/29528
ISBN: 0735400296
PURE UUID: da2460f3-3f40-4e2c-97db-ad689a587cfe

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

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Contributors

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

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