The Signed Monodromy Group of an Adinkra

TL;DR

This paper explores how the dashing of edges in an Adinkra influences its monodromy group, revealing a connection to Salingaros Vee groups through embeddings into Riemann surfaces.

Contribution

It introduces a signed permutation version of the monodromy group derived from Adinkra dashings and establishes its isomorphism to Salingaros Vee groups.

Findings

Signed permutation monodromy group determined by Adinkra dashings

Embedding of Adinkras into Riemann surfaces via colour ordering

Isomorphism between monodromy group and Salingaros Vee group

Abstract

An ordering of colours in an Adinkra leads to an embedding of this Adinkra into a Riemann surface $X$, and a branched covering map $\beta_X:X\to\mathbb{CP}^1$. This paper shows how the dashing of edges in an Adinkra determines a signed permutation version of the monodromy group, and shows that it is isomorphic to a Salingaros Vee group.