...matrices

see e.g. Sakurai [13], but note that our conventions differ from those of Jackson [14] for $Y_\ell^m$ by (-1)^m. The correspondence to [4] is $\, {}_{\pm 2}^{\vphantom{m}} Y_{\ell}^{m} = [(\ell-2)!/(\ell+2)!]^{1/2}[W_{(\ell m)} \pm i X_{(\ell m)}]$.

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...becomes,

Chandrasekhar employs a different sign convention for $U \rightarrow -U$.

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...HREF="node6.html#sec:radial">IIB,

Our conventions differ from [3] as $(2\ell+1)\Delta_{T\ell}^{(S,T)} = \Theta_\ell^{(0,2)}/(2\pi)^{3/2}$ and similarly for $\Delta_{E,B\ell}^{(S,T)}$ with $\Theta_\ell^{(0,2)} \rightarrow -E_\ell^{(0,2)}, -B_\ell^{(0,2)}$ and so $C_{C\ell}^{(S,T)} = - C_\ell^{\Theta E(0,2)}$ but with other power spectra the same.

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...$s=\pm 2$,

The expressions above were all derived assuming a flat spatial geometry. In this formalism, including the effects of spatial curvature is straightforward: the $\ell\pm 1$ terms in the hierarchy are multiplied by factors of $[1-(\ell^2 - m-1)K/k^2]^{1/2}$ [6,7], where the curvature is $K=-H_0^2(1-\Omega_{\rm tot})$. These factors account for geodesic deviation and alter the transfer of power through the hierarchy. A full treatment of such effects will be provided in [8].

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