Examples of pH in a sentence
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If λ : G —→ V h is such that λ(xp) = σh(p−1)λ(g), and∫⟨ ⟩f : G —→ V is such that f(gp) = σ(p−1)f(x), then the pairing is λ, f :=G/Pλ(x)(f(x))dx.When σ is unitary (or just has a nondegenerate form so that σ ⊂ σh), we getP ⊂ Ph viaG/Pg ∈ P '→ λg ∈ Ph, λg(f) = ∫ ⟨f(x), g(x)⟩dx for f ∈ P.
This is the delta- function supported on the coset mM0 taking constant value v.∈A typical element of P is given by δUxP,δmM0,v where U G/P is a neighborhood of the identity, the function satisfies the appropriate transformation law under P on the right, and the value at x is δmM0,v.If ψ ∈ HomG[P, P], then ψh ∈ HomG[Ph, Ph].
Aryl halides: (a) F– Ph, (b) Cl–Ph, (c) Br–Ph, and (d) I–Ph.Open Access Article.
But P admits a G—invariantpositive definite hermitian form, so while P Ph, nevertheless there is an inclusionPPσι : P —→ Ph. More precisely, if P = IndG σ, then the hermitian dual Ph is naturally isomorphic to IndG σh.