HepLean Documentation

HepLean.AnomalyCancellation.MSSMNu.Permutations

Permutations of MSSM charges and solutions #

The three family MSSM charges has a family permutation of S₃⁶. This file defines this group and its action on the MSSM.

The group of family permutations is S₃⁶

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    The type PermGroup has a group instances derived from the group instance of it's target.

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    The image of an element of permGroup under the representation on charges.

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    • One or more equations did not get rendered due to their size.
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      @[simp]
      theorem MSSM.chargeMap_apply (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
      (MSSM.chargeMap f) S = MSSMCharges.toSMPlusH.symm (MSSMCharges.splitSMPlusH.symm (MSSMCharges.toSpeciesMaps'.symm fun (i : Fin 6) => (MSSMCharges.toSMSpecies i) S (f i), MSSMCharges.toSMPlusH S Sum.inr))

      The representation of permGroup acting on the vector space of charges.

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        theorem MSSM.repCharges_toSMSpecies (f : MSSM.PermGroup) (S : MSSMCharges.Charges) (j : Fin 6) :
        (MSSMCharges.toSMSpecies j) ((MSSM.repCharges f) S) = (MSSMCharges.toSMSpecies j) S (f⁻¹ j)
        theorem MSSM.toSpecies_sum_invariant (m : ) (f : MSSM.PermGroup) (S : MSSMCharges.Charges) (j : Fin 6) :
        i : Fin MSSMSpecies.numberCharges, ((fun (a : ) => a ^ m) (MSSMCharges.toSMSpecies j) ((MSSM.repCharges f) S)) i = i : Fin MSSMSpecies.numberCharges, ((fun (a : ) => a ^ m) (MSSMCharges.toSMSpecies j) S) i
        theorem MSSM.Hd_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMCharges.Hd ((MSSM.repCharges f) S) = MSSMCharges.Hd S
        theorem MSSM.Hu_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMCharges.Hu ((MSSM.repCharges f) S) = MSSMCharges.Hu S
        theorem MSSM.accGrav_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accGrav ((MSSM.repCharges f) S) = MSSMACCs.accGrav S
        theorem MSSM.accSU2_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accSU2 ((MSSM.repCharges f) S) = MSSMACCs.accSU2 S
        theorem MSSM.accSU3_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accSU3 ((MSSM.repCharges f) S) = MSSMACCs.accSU3 S
        theorem MSSM.accYY_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accYY ((MSSM.repCharges f) S) = MSSMACCs.accYY S
        theorem MSSM.accQuad_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accQuad ((MSSM.repCharges f) S) = MSSMACCs.accQuad S
        theorem MSSM.accCube_invariant (f : MSSM.PermGroup) (S : MSSMCharges.Charges) :
        MSSMACCs.accCube ((MSSM.repCharges f) S) = MSSMACCs.accCube S