Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-09-26
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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