Inheritance of hyper-duality in imprimitive Bose-Mesner algebras

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 M and M denote Bose-Mesner algebras. Suppose there is a hyper-duality from the subconstituent algebra of M with respect to p to the subconstituent algebra of M with respect to p. Also suppose that M is imprimitive with respect to a subset I of Hadamard idempotents, so M is dual imprimitive with respect to the subset (I) of primitive idempotents, where : M M is the formal duality associated with . Let B denote the block Bose-Mesner algebra of M on the block containing p, and let Q denote the quotient Bose-Mesner algebra of M with respect to (I). Then there is a hyper-duality from the subconstituent algebra of B with respect to p to the subconstituent algebra of Q with respect to p. Key words: block Bose-Mesner algebra, quotient Bose-Mesner algebra, subconstituent algebra, Terwilliger algebra

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Brian Curtin
• Keywords: Algebra, Bose-mesner Algebra, DM 2008, Subconstituent Algebra