So I have been reading the famous paper on quantum field theory and Jones polynomial and have the following questions:

  1. On P.31 (381), it was said that the eigenvalues of $B$ are $$λ_i = ±\exp(i\pi(2h_R - h_{E_i})).\tag{4.18}$$ How is this formula derived? I know only a little conformal field theory, so please explain in more details.

  2. On P.40 (390), it was stated the matrix element of $S$ are $$S_{mn} = \sqrt{\dfrac{2}{k+2}}\sin\left(\dfrac{(m+1)(n+1)\pi}{k+2}\right).\tag{4.39}$$ Where does this equation come from?

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    $\begingroup$ anyone thinks I should ask the same question on Math Stack Exchange? Because this question is quite mathematical... $\endgroup$ – wilsonw Dec 16 '18 at 14:29

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