Inheritance of hyper-duality in imprimitive Bose–Mesner algebras Original Research Article

We prove the following result concerning the inheritance of hyper-duality by block and quotient Bose–Mesner algebras associated with a hyper-dual pair of imprimitive Bose–Mesner algebras. Let image and image denote Bose–Mesner algebras. Suppose there is a hyper-duality image from the subconstituent algebra of image with respect to p to the subconstituent algebra of image with respect to image. Also suppose that image is imprimitive with respect to a subset image of Hadamard idempotents, so image is dual imprimitive with respect to the subset image of primitive idempotents, where image is the formal duality associated with image. Let image denote the block Bose–Mesner algebra of image on the block containing p, and let image denote the quotient Bose–Mesner algebra of image with respect to image. Then there is a hyper-duality from the subconstituent algebra of image with respect to p to the subconstituent algebra of image with respect to image.