The Explicit Construction of Irreducible Representations of the Quantum Algebra Uq(sl(n))

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

The Explicit Construction of Irreducible Representations of the Quantum Algebra Uq(sl(n))

Original language description

The duality between the quantum algebra U-q(sl(n)) and the Hecke algebra H-m(q(2)) first pointed out by Jimbo is exploited to construct explicit irreducible representations of U-q(sl(n)). The method is based on the use of Young tableaux and involves thenotion 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 U-q(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 representationsare presented.

Czech name

The Explicit Construction of Irreducible Representations of the Quantum Algebra Uq(sl(n))

Czech description

The duality between the quantum algebra U-q(sl(n)) and the Hecke algebra H-m(q(2)) first pointed out by Jimbo is exploited to construct explicit irreducible representations of U-q(sl(n)). The method is based on the use of Young tableaux and involves thenotion 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 U-q(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 representationsare presented.

Type

D - Article in proceedings

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2001

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

NEW DEVELOPMENTS IN FUNDAMENTAL INTERACTION THEORIES

ISBN

0-7354-0029-6

ISSN

0094-243X

e-ISSN

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Number of pages

12

Pages from-to

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Publisher name

American Institute of Physics

Place of publication

Philadelphia

Event location

Karpacz

Event date

Feb 6, 2001

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000175882400013