Gauge Group subgroup ℤ₆ le ker rep Gauge Group I
StandardModel.DownSinglet.gaugeGroup_subgroup_ℤ₆_le_ker_repGaugeGroupI
Plain-language statement
The central ℤ₆ subgroup acts trivially on (3, 1)_{-2}.
Exact Lean statement
lemma gaugeGroup_subgroup_ℤ₆_le_ker_repGaugeGroupI :
GaugeGroupQuot.subgroup .ℤ₆ ≤ repGaugeGroupI.kerFormal artifact
Lean source
lemma gaugeGroup_subgroup_ℤ₆_le_ker_repGaugeGroupI : GaugeGroupQuot.subgroup .ℤ₆ ≤ repGaugeGroupI.ker := by simp only [GaugeGroupQuot.subgroup, gaugeGroupℤ₆SubGroup, SetLike.le_def, MonoidHom.mem_range, gaugeGroupℤ₆Hom_apply, Subtype.exists, mem_repGaugeGroupI_ker_iff_eq, forall_exists_index] rintro g x hx ⟨rfl⟩ use x ^ 2 simp only [gaugeGroupℤ₆OfRoot_toSU3, gaugeGroupℤ₆SU3OfRoot_eq_mul_id, gaugeGroupℤ₆OfRoot_toU1, gaugeGroupℤ₆UnitaryOfRoot_coe, true_and, RCLike.star_def, Complex.conj_rootsOfUnity hx, Units.val_inv_eq_inv_val, inv_pow] field_simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/StandardModel/Fermions/DownSinglet.lean:264-274
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