Fundamental domains for congruence subgroups of SL2 in positive characteristic

2009/09/01 by Lisa Carbone, Carbone, Lisa, Leigh Cobbs +3
Mathematics · #05C25 #20-04 #20E08 #20F32 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:05C25 #msc:20-04 #msc:20E08 #msc:20F32

paper · pdf · doi:10.48550/arxiv.0909.0062

arxiv created 2012/02/17 · arxiv updated 2012/02/20

Abstract

In this work, we construct fundamental domains for congruence subgroups of SL₂(F_q[t]) and PGL₂(F_q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat- Tits tree X = X_q+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma.

Related

• Connected fundamental domains for congruence subgroups
• Cusps and fundamental domains for congruence subgroups
• A topological realization of the congruence subgroup Kernel A
• On congruence subgroups of SL₂(ℤ[(1)/(p)]) generated by two parabolic elements
• Quotients of trees for arithmetic subgroups of PGL2 over a rational function field