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feat: Add reps to real modules

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jstoobysmith 2024-11-08 06:41:33 +00:00
parent 1350ab732d
commit 6b6f9261ca
4 changed files with 38 additions and 34 deletions
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8
HepLean/SpaceTime/LorentzVector/Complex/Basic.lean
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@ -37,8 +37,8 @@ def complexContr : Rep ℂ SL(2, ℂ) := Rep.of ContrℂModule.SL2CRep
def complexCo : Rep ℂ SL(2, ℂ) := Rep.of CoℂModule.SL2CRep
/-- The standard basis of complex contravariant Lorentz vectors. -/
def complexContrBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexContr := Basis.ofEquivFun
(Equiv.linearEquiv ℂ ContrℂModule.toFin13ℂFun)
def complexContrBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexContr :=
Basis.ofEquivFun ContrℂModule.toFin13ℂEquiv
@[simp]
lemma complexContrBasis_toFin13ℂ (i :Fin 1 ⊕ Fin 3) :
@ -65,8 +65,8 @@ def complexContrBasisFin4 : Basis (Fin 4) ℂ complexContr :=
Basis.reindex complexContrBasis finSumFinEquiv
/-- The standard basis of complex covariant Lorentz vectors. -/
def complexCoBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexCo := Basis.ofEquivFun
(Equiv.linearEquiv ℂ CoℂModule.toFin13ℂFun)
def complexCoBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexCo :=
Basis.ofEquivFun CoℂModule.toFin13ℂEquiv
@[simp]
lemma complexCoBasis_toFin13ℂ (i :Fin 1 ⊕ Fin 3) : (complexCoBasis i).toFin13ℂ = Pi.single i 1 := by