基于单项表示和上同调的形式正交对
Formal Orthogonal Pairs via Monomial Representations and Cohomology
摘要：
形式正交对是符号矩形矩阵对$(A,B)$，使得$AB^T=0$。它可以应用于Hadamard矩阵和加权矩阵的构造。在本文中，我们介绍了一个系统的方法来构建这样的对。我们的方法涉及到表示论和群上同调。正交性是某些上同调群之间的非零映射的结果。这种构造与关联方案和（加权）相干图理论有很强的联系。我们的技术也能够产生（反）友好对。举了几个例子。
英文摘要：
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.
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