■リー群と表現(その61)
三対性(三位一体性)について確認したい.
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[1]321
(56,756,4032,10080,12096,2016α5+4032α5,576(α6)+126(β6))
[2]231
(126,2016,10080,16128,756(β5)+4032(α5),56(221)+576α6)
[3]132
(576,10080,40320,50400,10080β4+16128α4,756hγ5+6048α5,56(122)+126hγ6)
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コクセターの論文で確認したところ
[2]231
(126,2016,10080,20160,16128(α4),756(β5)+4032(α5),56(221)+576α6)
[3]132
(576,10080,40320,50400,7560β4+16128α4,2268hγ5+2016α5,56(122)+126hγ6)
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