Construction of cyclic representations of quantum algebras at \(q^ p=1\) from their regular representations
Let \(L\) be a finite dimensional simple Lie algebra, and \(U_ qL\) the quantum algebra associated with \(L\), where \(q\) is the primitive \(p\)-th root of unity and \(p\) is an odd prime. In the present paper the authors construct the cyclic representation of maximal dimension for the quantum algebra \(U_ qsl(2)\), which is just that defined by De Concini and Kac. They then generalize the method of general \(U_ qL\), and construct the cyclic representation of maximal dimension for \(U_ qL\) from its regular representation. Furthermore, the cyclic representation for \(U_ qsl(3)\) is also constructed. This work is a continuation of several mathematicians' work in this direction.
scientific article; zbMATH DE number 97829