MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS

Year 2020, Volume: 28 Issue: 28, 156 - 174, 14.07.2020

Deepak Naıdu

https://doi.org/10.24330/ieja.768210

Abstract

We show that the image of the representation of the modular group $\SL(2, \Z)$ arising from the representation category $\Rep(D(G))$ of the Drinfeld double $D(G)$
is isomorphic to the group $\PSL(2, \Zn) \times S_3$, when $G$ is either the dihedral group of order $2n$ or the dihedral group of order $4n$ for some odd integer $n \geq 3$. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Keywords

Drinfeld double, modular tensor category, modular group, congruence subgroup

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