Weights on homogeneous coherent configurations

TL;DR

This paper explores weights on homogeneous coherent configurations, establishing a link to group cohomology and generalizing Higman's construction via monomial representations of finite groups.

Contribution

It introduces a modified definition of weights on coherent configurations and connects them to group cohomology, extending Higman's method to a broader context.

Findings

Weights on thin homogeneous configurations correspond to group cohomology classes.

A new construction of weights generalizes Higman's approach using monomial representations.

The study bridges coherent configurations with finite group theory and cohomology.

Abstract

D. G. Higman generalized a coherent configuration and defined a weight. In this article, we will modify the definition and investigate weights on coherent configurations. If our weights are on a thin homogeneous coherent configuration, that is essentially a finite group, then there is a natural correspondence between the set of equivalence classes of weights and $2$-cohomology group of the group. We also give a construction of weights as a generalization of Higman's method using monomial representations of finite groups.