# Krein parameters of fiber-commutative coherent configurations

## TL;DR

This paper demonstrates that Krein parameters for fiber-commutative coherent configurations are essentially unique, simplifying the Krein condition and the absolute bound, with implications for generalized quadrangles.

## Contribution

It establishes the essential uniqueness of Krein parameters in fiber-commutative coherent configurations and simplifies related bounds and conditions.

## Key findings

- Krein parameters are essentially uniquely defined for fiber-commutative coherent configurations.
- The Krein condition reduces to checking positive semidefiniteness of finitely many matrices.
- Simplified absolute bound using matrices of Krein parameters.

## Abstract

For fiber-commutative coherent configurations, we show that Krein parameters can be defined essentially uniquely. As a consequence, the general Krein condition reduces to positive semidefiniteness of finitely many matrices determined by the parameters of a coherent configuration. We mention its implications in the coherent configuration defined by a generalized quadrangle. We also simplify the absolute bound using the matrices of Krein parameters.