Fan, splint and branching rules

TL;DR

This paper explores how splint structures of root systems in simple Lie algebras can be used to simplify the calculation of branching rules and coefficients in algebraic embeddings.

Contribution

It demonstrates that implementing splint properties significantly reduces the complexity of computing branching coefficients in Lie algebra embeddings.

Findings

Splint properties enable simplified calculations of branching coefficients.

Application of splints aids in understanding regular embeddings of reductive subalgebras.

The approach streamlines algebraic computations in Lie theory.

Abstract

Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching rules. We demonstrate that splint properties implementation drastically simplify calculations of branching coefficients.