INDUCED MODULE CONSTRUCTION FOR HIGHEST-WEIGHT REPRESENTATIONS OF U(Q)(GL(N)) AT ROOTS OF UNITY

A method is investigated for inducing highest-weight representations f or the quantum group U(q)(gl(n)) from the canonical subalgebra U(q)(gl (n - 1)) when q is a root of unity. We classify the irreps into two ty pes, typical and atypical, where the former is a generalization of the class of irreps with maximal dimensionality. The structures of both t he typical and atypical irreps are studied; in particular, a sufficien cy condition is given for an irrep to be typical. As examples, we cons ider flat representations induced from a one-dimensional representatio n of the canonical subalgebra and representations induced from vector representation.