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1970•Journal of Mathematical PhysicsRequires access

Labeling States and Constructing Matrix Representations of G2

J. Patera

Open publisher page 13 citations

Abstract

A method is developed for labeling G2-internal states and for finding the matrices representing G2-generators. The simple Lie algebra G2 is embedded into A6, whose representation spaces are labeled by Gel'fand patterns. For a given irreducible finite-dimensional representation Ψ(G2) of G2, an optimal representation Φ(A6)⊃Ψ(G2) is chosen, and a lemma is formulated which enables us to select the subspace R(Ψ) from the representation space R(Φ).

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What this paper is about

A method is developed for labeling G2-internal states and for finding the matrices representing G2-generators. The simple Lie algebra G2 is embedded into A6, whose representation spaces are labeled by Gel'fand patterns. For a given irreducible finite-dimensional representation Ψ(G2) of G2, an optimal representation Φ(A6)⊃Ψ(G2) is chosen, and a lemma is formulated which enables us to select the subspace R(Ψ) from the representation space R(Φ).

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Available abstract

A method is developed for labeling G2-internal states and for finding the matrices representing G2-generators. The simple Lie algebra G2 is embedded into A6, whose representation spaces are labeled by Gel'fand patterns. For a given irreducible finite-dimensional representation Ψ(G2) of G2, an optimal representation Φ(A6)⊃Ψ(G2) is chosen, and a lemma is formulated which enables us to select the subspace R(Ψ) from the representation space R(Φ).

Key concepts: Representation (politics), Irreducible representation, Subspace topology, Lemma (botany), Mathematics, Algebra over a field, Trivial representation, Representation theory of SU

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