Kac--Moody Fibonacci sequences

TL;DR

This paper reviews methods to generate infinite Fibonacci-like sequences from rank 2 Kac--Moody algebra root lattices, providing a comprehensive framework and tabulated data for these sequences and related polynomial evaluations.

Contribution

It introduces a unified framework for generating and analyzing Fibonacci-type sequences from Kac--Moody algebra root lattices, with explicit tabulations and connections to Chebyshev polynomials.

Findings

Generated first twenty entries of multiple sequences

Established connections to Chebyshev S and U-polynomials

Provided a comprehensive framework for Fibonacci-type sequences

Abstract

We summarize known results on how to generate an infinite family of integer sequences from the root lattices of rank 2 Kac--Moody algebras. We compute and tabulate the first twenty entries of a number of these sequences. This provides an overarching framework for a large class of Fibonacci-type integer sequences, evaluations of Chebyshev S and U-polynomials and others.