Explicit Belyi maps over Q having almost simple primitive monodromy groups

TL;DR

This paper classifies specific Belyi maps with almost simple primitive monodromy groups over the complex projective line, identifying new polynomials with these Galois groups over Q(t).

Contribution

It provides a complete list of Belyi maps with certain monodromy groups and degrees, expanding the understanding of Galois groups over Q(t).

Findings

All such Belyi maps with specified properties are classified.

New polynomials with almost simple Galois groups over Q(t) are constructed.

The degree range of these maps is between 50 and 250.

Abstract

We present all Belyi maps P^1(C) -> P^1(C) having almost simple primitive monodromy groups (not isomorphic to A_n or S_n) containing rigid and rational generating triples of degree between 50 and 250. This also leads to new polynomials having almost simple Galois groups over Q(t).