Séminaire Lotharingien de Combinatoire, 84B.68 (2020), 12 pp.

Assaf Goldberger and Ilias Kotsireas

Formal Orthogonal Pairs Via Monomial Representations and Cohomology

Abstract. A formal orthogonal pair is a pair (A,B) of symbolic rectangular matrices such that AB^T=0. It can be applied for the construction of Hadamard and weighing matrices. In this paper we introduce a systematic way for constructing such pairs. Our method involves representation theory and group cohomology. The orthogonality property is a consequence of non-vanishing maps between certain cohomology groups. This construction has strong connections to the theory of association schemes and (weighted) coherent configurations. Our techniques are also capable for producing (anti-) amicable pairs. A handful of examples are given.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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