Irreducible Representations of Cayley-Klein Orthogonal Algebras

TL;DR

This paper studies how irreducible representations of Cayley-Klein orthogonal algebras behave under multidimensional contractions, revealing isomorphisms and different basis representations.

Contribution

It introduces a method of transitions to describe reducible representations across different bases during algebra contractions.

Findings

Contractions can lead to isomorphic algebras.

Different bases can represent the same reducible representations.

The method of transitions links discrete and continuous bases.

Abstract

Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of transitions describes the same reducible representations in different basises, say discrete and continuons ones.