eldorado.tu-dortmund.de/server/api/core/bitstreams/f7043a77-8f49-4038-95d6-3fec1dc5f1c7/content
calculation
ζ(k−1v1, . . . , k −1vq) = ζ(k−1Φ−1(Φ(v1)), . . . , k−1Φ−1(Φ(vq)))
= Ψ−1(Ψζ)(k−1Φ−1(v1), . . . , k−1Φ−1(vq))
= (Ψ−1ξ)(k−1Φ−1(v1), . . . , k−1Φ−1(vq)) (1.6)= ξ((ΦkΦ−1)−1(v1) . . . , (ΦkΦ−1)−1(vq)),
where [...] have
ps([δ1,0, δ1,0∗])(x, θ)ζx = θ1,0 ⊙ (θ0,1)# ⌟ ζx − (θ0,1)# ⌟ θ1,0 ⊙ ζx
= −g(θ1,0, θ0,1) ζx
= −1
2 g(θ, θ)ζx
ps([δ0,1, δ0,1∗])(x, θ)ζx = θ0,1 ⊙ (θ1,0)# ⌟ ζx − (θ1,0)# ⌟ θ0,1 ⊙ ζx
= −g(θ0,1, θ̄1,0) ζx
= [...] ζ)
and by writing ζ = ∑ ζi1...iq ϕi1 ⊙⋯⊙ ϕiq we obtain the desired expression for R(ζ)
R(ζ)j1⋯jq = n
∑ i=1
q
∑ s=1
ricjsi ζj1⋯js−1ijs+1⋯jq − n
∑ i,k=1
q
∑ r,s=1 r≠s
Rk ijsjr ζj1⋯js−1ijs+1⋯jr−1kjr+1⋯jq …
