This Review details the relationship between the isomonodromic tau-function and conformal blocks on a torus with one simple pole. It is based on the author’s talk at ICMP 2021.

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31.

The reason behind this is computational and is detailed in Refs. 5 and 7.

32.

For the ease of notation, we the keep the notation of the kernels a,b,c,d.

33.

The explicit form of the Fourier coefficients as;βr;α,bs;βr;α,cs;βr;α,ds;βr;α is not relevant for the purposes of this Review but is computed in Ref. 5.

34.

Since sI, the hole positions in the corresponding Maya diagram m are h(m)=s1,,sk, and since r ∈ J, the particle positions are p(m)=r1,,rl.

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Refer to Eq. (2.45) in Ref. 7 for the full computation.

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