Representations of \( sl_{q} (3) \) at the roots of unity

Cantarini, Nicoletta

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 4, pp. 201-212

Résumé

In this paper we study the irreducible finite dimensional representations of the quantized enveloping algebra \( \mathcal{U}_{q} (g) \) associated to \( g = sl (3) \), at the roots of unity. It is known that these representations are parametrized, up to isomorphisms, by the conjugacy classes of the group \( G = SL(3) \). We get a complete classification of the representations corresponding to the submaximal unipotent conjugacy class and therefore a proof of the De Concini-Kac conjecture about the dimension of the \( \mathcal{U}_{q} (g) \)-modules at the roots of \( 1 \) in the case of \( g = sl (3) \).