Representations of U_q(sl(N)) at Roots of Unity

Abstract

The Gelfand--Zetlin basis for representations of $U_q(sl(N))$ is improved to fit better the case when $q$ is a root of unity. The usual $q$-deformed representations, as well as the nilpotent, periodic (cyclic), semi-periodic (semi-cyclic) and also some atypical representations are now described with the same formalism.

18 pages, Plain TeX, Macros harvmac.tex and epsf needed 3 figures in a uuencoded tar separate file. Some references are added. Also available at http://lapphp0.in2p3.fr/preplapp/psth/uqsln.ps.gz

References in corpus (3)

• Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: II. Nontypical representations at generic $q$
• Roots of Unity: Representations of Quantum Groups
• Polynomial Relations in the Centre of U_q(sl(N))

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• Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1
• Overview of knot invariants at roots of unity