http://www.neverendingbooks.org/index.php/hyperbolic-mathieu-polygons.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 http://www.neverendingbooks.org/index.php/hyperbolic-mathieu-polygons.html/comment-page-1#comment-9802 the modular group and superpotentials (1) | neverendingbooks Thu, 09 Dec 2010 14:53:44 +0000 http://www.neverendingbooks.org/?p=20#comment-9802 [...] Here I will go over the last post at a more leisurely pace, focussing on a couple of far more trivial examples. Here’s the goal : we want to assign a quiver-superpotential to any subgroup of finite index of the modular group. So fix such a subgroup of the modular group and consider the associated permutation representation of on the left-cosets . As this representation is determined by the action of the order 2 and order 3 generators of the modular group. There are a number of combinatorial gadgets to control the subgroup and the associated permutation representation : (generalized) Farey symbols and dessins d’enfants. [...] [...] Here I will go over the last post at a more leisurely pace, focussing on a couple of far more trivial examples. Here’s the goal : we want to assign a quiver-superpotential to any subgroup of finite index of the modular group. So fix such a subgroup of the modular group and consider the associated permutation representation of on the left-cosets . As this representation is determined by the action of the order 2 and order 3 generators of the modular group. There are a number of combinatorial gadgets to control the subgroup and the associated permutation representation : (generalized) Farey symbols and dessins d’enfants. [...]

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