Gauge-Higgs Unification Models in Six Dimensions with 𝑆²/𝑍₂ Extra Space and GUT Gauge Symmetry

Table 2

Commutation relations of 𝑄_𝛼, 𝑄_{𝑋,𝑌,𝐼}, 𝑄_{𝑥(3,−3,3)} and 𝑄^{𝑥(−3,3,−3)}, where 𝜎_𝑖 are the Pauli matrices.

[𝑄𝑥(3,−3,3),𝑄^𝑦(−3,3,−3)1]=2𝛿^𝑦𝑥𝑄𝐼−1235𝛿^𝑦𝑥𝑄𝑋+1√𝛿10^𝑦𝑥𝑄𝑌+1√6(𝜎𝛼)^𝑦𝑥𝑄𝛼
[𝑄𝛼,𝑄𝑥(3,−3,3)1]=√6(𝜎𝛼)^𝑦𝑥𝑄𝑦(3,−3,3),	[𝑄𝛼,𝑄^𝑥(−3,3,−3)1]=−√6(𝜎^∗𝛼)^𝑦𝑥𝑄^𝑦(−3,3,−3),
[𝑄𝑥(3,−3,3),𝑄𝑦(3,−3,3)]=0,	[𝑄𝐼,𝑄𝑥(3,−3,3)1]=2𝑄𝑥(3,−3,3),
[𝑄𝑋,𝑄𝑥(3,−3,3)1]=−235𝑄𝑥(3,−3,3),	[𝑄𝑌,𝑄𝑥(3,−3,3)1]=√𝑄10^𝑥(3,−3,3),