Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

Constructive Fourier realization

An explicit abelian local-system category › Constructive Fourier realization · lines 518–532

Oai069-A@1#eq:fourier

On $S = C^{d}$ , define

S_{a} ∣ j ⟩ = ∣ j + a ⟩, Z_{b} ∣ j ⟩ = ω^{bj} ∣ j ⟩,

and

F_{d} ∣ j ⟩ = \frac{1}{d} k = 0 \sum^{d - 1} ω^{k j} ∣ k ⟩, v_{k} = \frac{1}{d} j = 0 \sum^{d - 1} ω^{- k j} ∣ j ⟩ .

Displayed formulas in this passage

Oai069-A@1#eq:fourier · line 526
$F_{d} ∣ j ⟩ = \frac{1}{d} k = 0 \sum^{d - 1} ω^{k j} ∣ k ⟩, v_{k} = \frac{1}{d} j = 0 \sum^{d - 1} ω^{- k j} ∣ j ⟩ .$
unlabeled · line 521
$S_{a} ∣ j ⟩ = ∣ j + a ⟩, Z_{b} ∣ j ⟩ = ω^{bj} ∣ j ⟩,$