Euler's triangle and the decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra

TL;DR

This paper explores the connection between Euler's trinomial problem and the decomposition of tensor powers of the adjoint representation of the $A_1$ Lie algebra, yielding new insights into both mathematical problems.

Contribution

It introduces a novel approach linking Euler's trinomial problem with tensor power decompositions in Lie algebra representation theory, producing new results.

Findings

New results for Euler's trinomial problem

Decomposition formulas for tensor powers of $A_1$ adjoint representation

Established connection between two classical problems

Abstract

We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.