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A finite subgroup of the exceptional Lie group G2

A finite subgroup of the exceptional Lie group G2
A finite subgroup of the exceptional Lie group G2
With a view to further refining the use of the exceptional group G2 in atomic and nuclear spectroscopy, it is confirmed that a simple finite subgroup L168~PSL2(7) of order 168 of the symmetric group S8 is also a subgroup of G2. It is established by character theoretic and other methods that there are two distinct embeddings of L168 in G2, analogous to the two distinct embeddings of SO(3) in G2. Relevant branching rules, tensor products and symmetrized tensor products are tabulated. As a stimulus to further applications the branching rules are given for the restriction from L168 to the octahedral crystallographic point group O.
0305-4470
8527-8537
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Toumazet, F.
e49842d7-7844-4104-a7d4-be92a2659a6a
Wybourne, B.G.
527c5e72-79db-40a6-901c-284a3bd788dc
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Toumazet, F.
e49842d7-7844-4104-a7d4-be92a2659a6a
Wybourne, B.G.
527c5e72-79db-40a6-901c-284a3bd788dc

King, R.C., Toumazet, F. and Wybourne, B.G. (1999) A finite subgroup of the exceptional Lie group G2. Journal of Physics A: Mathematical and General, 32 (48), 8527-8537. (doi:10.1088/0305-4470/32/48/312).

Record type: Article

Abstract

With a view to further refining the use of the exceptional group G2 in atomic and nuclear spectroscopy, it is confirmed that a simple finite subgroup L168~PSL2(7) of order 168 of the symmetric group S8 is also a subgroup of G2. It is established by character theoretic and other methods that there are two distinct embeddings of L168 in G2, analogous to the two distinct embeddings of SO(3) in G2. Relevant branching rules, tensor products and symmetrized tensor products are tabulated. As a stimulus to further applications the branching rules are given for the restriction from L168 to the octahedral crystallographic point group O.

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More information

Published date: 1999
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29520
URI: http://eprints.soton.ac.uk/id/eprint/29520
ISSN: 0305-4470
PURE UUID: 3dd3dacc-fc43-4f91-8fe2-dec9546b1ebd

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Date deposited: 21 Dec 2006
Last modified: 15 Jul 2019 19:08

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