We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of *{\cal U}_{\displaystyle{q}}(sl(N))* when *q* is root of unity. The explicit construction of atypical representation is presented in details for *N=3*.

September 13, 1995

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Atypical Representations of $U_{q}(sl(N))$ at Roots of Unity

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