Fundamental domains for congruence subgroups of SL2 in positive characteristic

Lisa Carbone; Leigh Cobbs; Scott Murray

doi:10.1016/J.JALGEBRA.2010.08.028

Fundamental domains for congruence subgroups of SL2 in positive characteristic

Lisa Carbone, Leigh Cobbs, Scott Murray

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+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

Original language	English
Pages (from-to)	431-439
Number of pages	9
Journal	Journal of Algebra
Volume	325
Issue number	1
DOIs	https://doi.org/10.1016/J.JALGEBRA.2010.08.028
Publication status	Published - 2011

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title = "Fundamental domains for congruence subgroups of SL2 in positive characteristic",

abstract = "In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+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",

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author = "Lisa Carbone and Leigh Cobbs and Scott Murray",

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T1 - Fundamental domains for congruence subgroups of SL2 in positive characteristic

AU - Carbone, Lisa

AU - Cobbs, Leigh

AU - Murray, Scott

PY - 2011

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N2 - In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+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

AB - In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+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

KW - Groups acting on trees

U2 - 10.1016/J.JALGEBRA.2010.08.028

DO - 10.1016/J.JALGEBRA.2010.08.028

M3 - Article

SN - 0021-8693

VL - 325

SP - 431

EP - 439

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Fundamental domains for congruence subgroups of SL2 in positive characteristic

Abstract

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