A Classification of Unitary Highest Weight Modules of the Quantum Analogue of the Symmetric Pair (An, An − 1) Original Research Article

We study the irreducibility and unitarity of highest weight modules of the quantized enveloping algebra associated to imageimage(n, 1). We obtain a classification of these modules analogous to that of [EHW] in the classical context. We also compute all commutation relations between root vectors in imageq(imageimage(n, 1)).