# Formal Orthogonal Pairs via Monomial Representations and Cohomology

@article{Goldberger2020FormalOP, title={Formal Orthogonal Pairs via Monomial Representations and Cohomology}, author={Assaf Goldberger and I. Kotsireas}, journal={arXiv: Combinatorics}, year={2020} }

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… Expand

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