On affine extension of splint root systems

TL;DR

This paper explores the affine extension of splint root systems in simple Lie algebras, providing new relations on theta and branching functions to simplify calculations of branching coefficients.

Contribution

It introduces the affine extension of splint root systems and derives relations on theta and branching functions, advancing the understanding of Lie algebra embeddings.

Findings

Derived relations on theta functions and branching functions.

Simplified calculations of branching coefficients.

Enhanced understanding of affine splint root systems.

Abstract

Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application of splint properties drastically simplifies calculations of branching coefficients. We study affine extension of splint root system of simple Lie algebra and obtain relations on theta and branching functions.