论文标题
正式对正交对通过单一表示和共同学
Formal Orthogonal Pairs via Monomial Representations and Cohomology
论文作者
论文摘要
正式的正交对是一对$（a，b）符号矩形矩阵，以便$ ab^t = 0 $。它可以应用于Hadamard和称重矩阵的构造。在本文中，我们介绍了一种构建此类对的系统方法。我们的方法涉及代表理论和群体的共同体。正交性属性是某些共同体学组之间非变化图的结果。该结构与关联方案和（加权）相干配置的理论有很强的联系。我们的技术也能够产生（反）友好对。给出了少数例子。
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.
