MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS

Authors : Deepak NAIDU

Pages : 156-174

Doi:10.24330/ieja.768210

View : 12 | Download : 14

Publication Date : 2020-07-14

Article Type : Research Paper

Abstract :We show that the image of the representation of the modular group $\SLinsert ignore into journalissuearticles values(2, \Z);$ arising from the representation category $\Repinsert ignore into journalissuearticles values(Dinsert ignore into journalissuearticles values(G););$ of the Drinfeld double $Dinsert ignore into journalissuearticles values(G);$ is isomorphic to the group $\PSLinsert ignore into journalissuearticles values(2, \Zn); \times S_3$, 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