Tag: congruence subgroup

  • Monstrous dessins 3

    A long while ago I promised to take you from the action by the modular group $\Gamma=PSL_2(\mathbb{Z})$ on the lattices at hyperdistance $n$ from the standard orthogonal laatice $L_1$ to the corresponding ‘monstrous’ Grothendieck dessin d’enfant. Speaking of dessins d’enfant, let me point you to the latest intriguing paper by Yuri I. Manin and Matilde […]

  • Snakes, spines, threads and all that

    Conway introduced his Big Picture to make it easier to understand and name the groups appearing in Monstrous Moonshine. For $M \in \mathbb{Q}_+$ and $0 \leq \frac{g}{h} < 1$, $M,\frac{g}{h}$ denotes (the projective equivalence class of) the lattice \[ \mathbb{Z} (M \vec{e}_1 + \frac{g}{h} \vec{e}_2) \oplus \mathbb{Z} \vec{e}_2 \] which we also like to represent…