Classical semisimplicity conjecture for the exceptional series

Let UU be a subset of C\mathbb C, and let the Cauchy completion mean the additive and idempotent completion of a category. Classical semisimplicity conjecture. There is a dense subset UCU\subset\mathbb C such that, for every λU\lambda\in U, the Cauchy completion of ExcC,λ\mathsf{Exc}_{\mathbb C,\lambda} is semisimple. This predicts generic semisimplicity of the classical exceptional family; the source uses the standard topology on C\mathbb C and expects that infinitely many polynomial inversions may be needed.

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Primary source

Kim Morrison, Noah Snyder and Dylan P. Thurston, “Towards the quantum exceptional series”, arXiv:2402.03637 (2025).

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