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Mar 1, 2022 at 14:15 comment added Konrad Waldorf The criterion is Prop. 4.4.5 in Pressley-Segal, saying that the product of a coroot with itself is in $2\mathbb{Z}$.
Feb 28, 2022 at 15:25 comment added Adrien Indeed, I'd say the point is that this is really a condition on the parameter $k$ (in the sense that one usually assume the normalization of the pairing is chosen once and for all but then $k$ may vary).
Feb 28, 2022 at 15:12 history edited G. Blaickner CC BY-SA 4.0
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Feb 28, 2022 at 15:01 history edited G. Blaickner CC BY-SA 4.0
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Feb 28, 2022 at 14:36 history asked G. Blaickner CC BY-SA 4.0