Fundamental representations of quantum groups at roots of 1

✍ Scribed by Vyjayanthi Chari; Andrew Pressley

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 497 KB
• Volume: 26
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00398810

✦ Synopsis

To every fimte-dlmensional irreducible representation V of the quantum group U,(g_) where e is a primitive /th root of unity (1 odd) and g is a finite-dimensional complex simple Lie algebra, de Concini, Kac and Procesi have associated a conjugacy class C v in the adjoint group G ofg. We describe exphcltly, when g is of type A,, B n, Cn, or D 4, the representations assooated to the con lugacy classes of mimmal positive dimension. We call such representations fundamental and prove that, for any conjugacy class, there is an associated representation which is contained in a tensor product of fundamental representations.