Generalized Verlinde formulae for some Riemann surface automorphisms

Details Generalized Verlinde formulae for some Riemann surface automorphisms Generalized Verlinde formulae for some Riemann surface automorphisms

2003-09-26

arxiv.org/abs/hep-th/0309247v3

Lett.Math.Phys. 68 (2004) 91-102

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, minor changes

Scientific paper

10.1023/B:MATH.0000043319.80193.

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 $\mathcal{X}(11)$, and a factor curve of $\mathcal{X}(8)$. 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.

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