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Modular linear differential equations of fourth order and minimal mathcal{W}-algebras

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arxiv 1803.02022 v1 pith:PWIBDPCE submitted 2018-03-06 math.QA math.NT

Modular linear differential equations of fourth order and minimal mathcal{W}-algebras

classification math.QA math.NT
keywords differentialequationsalgebrasmathcalminimalordercharacterizationdeligne
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A characterization of the minimal $\mathcal{W}$-algebras associated with the Deligne exceptional series at level $-h^\vee/6$ is obtained by using one-parameter family of modular linear differential equations of order $4$. In particular, the characters of the Ramond-twisted modules of minimal $\mathcal{W}$-algebras related to the Deligne exceptional series satisfy one of these differential equations. In order to obtain the characterization, the differential equations in the one parameter family which have solutions of "CFT type" are classified, whose solutions are explicitly described.

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