Uniqueness conjecture for the Rudvalis enhanced VOA with prescribed local algebra

From papers

Let (U,Y,1,Ω)(U,Y,{\bf 1},\Omega) be a nice rational enhanced VOA with local algebra A(Ω)A(Ω\textslRu)\mathcal{A}(\Omega)\cong\mathcal{A}(\Omega_{\operatorname{\textsl{Ru}}}). Assume that UU has rank 2828, is self-dual, and that U1ˉU_{\bar{1}} has no non-trivial vectors of degree less than 7/27/2. Uniqueness conjecture. Then

(U,Y,1,Ω)(A\textslRu,Y,1,Ω\textslRu).(U,Y,{\bf 1},\Omega)\cong(A_{{\operatorname{\textsl{Ru}}}},Y,{\bf 1},\Omega_{\operatorname{\textsl{Ru}}}).

This is the precise formal version of the proposed characterization of the Rudvalis enhanced VOA. The surrounding discussion says that the hypotheses force the character, while the claimed isomorphism remains conjectural.

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Sources & referencesView supporting material

Primary source

John F. Duncan, “Moonshine for Rudvalis's sporadic group I”, arXiv:math/0609449 (2008).

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