Euler's difference table and the decomposition of tensor powers of the adjoint representation of the $A_n$ Lie algebra

A. M. Perelomov

Institute for Theoretical and Experimental Physics named by A. I. Alikhanov of National Research Centre "Kurchatov Institute», Moscow, Russia

Abstract: By using Euler's difference table, we obtain a simple explicit formula for the decomposition of the $k$th tensor power of the adjoint representation of the $A_n$ Lie algebra at $2k\le n+1$.

Keywords: Lie algebras, representation theory.

Received: 13.09.2022
Revised: 13.09.2022

DOI: 10.4213/tmf10368

 English version: Theoretical and Mathematical Physics, 2022, 213:3, 1665–1668

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