Generalized Verlinde formulae for some Riemann surface automorphisms

DOI10.1023/B:MATH.0000043319.80193.68zbMATH Open1084.81068arXivhep-th/0309247OpenAlexW3101655565MaRDI QIDQ2575235

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Publication date: 8 December 2005

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Abstract: The generalized Verlinde formulae expressing traces of mapping classes corresponding to automorphisms of certain Riemann surfaces, and the congruence relations on allowed modular representations following from them are presented. The surfaces considered are families of algebraic curves given by suitably chosen equations, the modular curve $mathcalX(11)$, and a factor curve of $mathcalX(8)$. The examples of modular curves illustrate how the study of arithmetic properties of suitable modular representations can be used to gain information on automorphic properties of Riemann surfaces.

Full work available at URL: https://arxiv.org/abs/hep-th/0309247

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