| {"name":"MSSM.PermGroup","declaration":"/-- The group of family permutations is `S₃⁶`-/\ndef MSSM.PermGroup : Type"} | |
| {"name":"MSSM.accSU2_invariant","declaration":"theorem MSSM.accSU2_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accSU2 ((MSSM.repCharges f) S) = MSSMACCs.accSU2 S"} | |
| {"name":"MSSM.accSU3_invariant","declaration":"theorem MSSM.accSU3_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accSU3 ((MSSM.repCharges f) S) = MSSMACCs.accSU3 S"} | |
| {"name":"MSSM.accCube_invariant","declaration":"theorem MSSM.accCube_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accCube ((MSSM.repCharges f) S) = MSSMACCs.accCube S"} | |
| {"name":"MSSM.Hu_invariant","declaration":"theorem MSSM.Hu_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMCharges.Hu ((MSSM.repCharges f) S) = MSSMCharges.Hu S"} | |
| {"name":"MSSM.accQuad_invariant","declaration":"theorem MSSM.accQuad_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accQuad ((MSSM.repCharges f) S) = MSSMACCs.accQuad S"} | |
| {"name":"MSSM.accGrav_invariant","declaration":"theorem MSSM.accGrav_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accGrav ((MSSM.repCharges f) S) = MSSMACCs.accGrav S"} | |
| {"name":"MSSM.chargeMap","declaration":"/-- The image of an element of `permGroup` under the representation on charges. -/\ndef MSSM.chargeMap (f : MSSM.PermGroup) : ACCSystemCharges.Charges MSSMCharges →ₗ[ℚ] ACCSystemCharges.Charges MSSMCharges"} | |
| {"name":"MSSM.repCharges_toSMSpecies","declaration":"theorem MSSM.repCharges_toSMSpecies (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) (j : Fin 6) : (MSSMCharges.toSMSpecies j) ((MSSM.repCharges f) S) = (MSSMCharges.toSMSpecies j) S ∘ ⇑(f⁻¹ j)"} | |
| {"name":"MSSM.instGroupPermGroup","declaration":"instance MSSM.instGroupPermGroup : Group MSSM.PermGroup"} | |
| {"name":"MSSM.chargeMap_apply","declaration":"theorem MSSM.chargeMap_apply (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : (MSSM.chargeMap f) S =\n MSSMCharges.toSMPlusH.symm\n (MSSMCharges.splitSMPlusH.symm\n (MSSMCharges.toSpeciesMaps'.symm fun i => (MSSMCharges.toSMSpecies i) S ∘ ⇑(f i),\n MSSMCharges.toSMPlusH S ∘ Sum.inr))"} | |
| {"name":"MSSM.toSpecies_sum_invariant","declaration":"theorem MSSM.toSpecies_sum_invariant (m : ℕ) (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) (j : Fin 6) : (Finset.sum Finset.univ fun i => ((fun a => a ^ m) ∘ (MSSMCharges.toSMSpecies j) ((MSSM.repCharges f) S)) i) =\n Finset.sum Finset.univ fun i => ((fun a => a ^ m) ∘ (MSSMCharges.toSMSpecies j) S) i"} | |
| {"name":"MSSM.repCharges","declaration":"/-- The representation of `permGroup` acting on the vector space of charges. -/\ndef MSSM.repCharges : Representation ℚ MSSM.PermGroup (ACCSystemCharges.Charges MSSMCharges)"} | |
| {"name":"MSSM.accYY_invariant","declaration":"theorem MSSM.accYY_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMACCs.accYY ((MSSM.repCharges f) S) = MSSMACCs.accYY S"} | |
| {"name":"MSSM.Hd_invariant","declaration":"theorem MSSM.Hd_invariant (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) : MSSMCharges.Hd ((MSSM.repCharges f) S) = MSSMCharges.Hd S"} | |
| {"name":"MSSM.chargeMap_toSpecies","declaration":"theorem MSSM.chargeMap_toSpecies (f : MSSM.PermGroup) (S : ACCSystemCharges.Charges MSSMCharges) (j : Fin 6) : (MSSMCharges.toSMSpecies j) ((MSSM.chargeMap f) S) = (MSSMCharges.toSMSpecies j) S ∘ ⇑(f j)"} | |