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.
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
1999
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), .
(doi:10.1088/0305-4470/32/48/312).
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.
This record has no associated files available for download.
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
Catalogue record
Date deposited: 21 Dec 2006
Last modified: 15 Mar 2024 07:32
Export record
Altmetrics
Contributors
Author:
R.C. King
Author:
F. Toumazet
Author:
B.G. Wybourne
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics