TY - GEN
T1 - Picard modular groups generated by complex reflections
AU - Mark, Alice
AU - Paupert, Julien
AU - Polletta, David
N1 - Funding Information:
Second author partially supported by National Science Foundation Grant DMS-1708463.
Publisher Copyright:
© 2023 American Mathematical Society.
PY - 2023
Y1 - 2023
N2 - In this short note we use the presentations found by the various authors to show that the Picard modular groups PU(2, 1, Od ) with d = 1, 3, 7 (respectively the quaternion hyperbolic lattice PSp(2, 1, H) with entries in the Hurwitz integer ring H) are generated by complex (resp. quaternionic) reflections, and that the Picard modular groups PU(2, 1, Od ) with d = 2, 11 have an index 4 subgroup generated by complex reflections.
AB - In this short note we use the presentations found by the various authors to show that the Picard modular groups PU(2, 1, Od ) with d = 1, 3, 7 (respectively the quaternion hyperbolic lattice PSp(2, 1, H) with entries in the Hurwitz integer ring H) are generated by complex (resp. quaternionic) reflections, and that the Picard modular groups PU(2, 1, Od ) with d = 2, 11 have an index 4 subgroup generated by complex reflections.
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U2 - 10.1090/conm/783/15735
DO - 10.1090/conm/783/15735
M3 - Conference contribution
AN - SCOPUS:85152941514
SN - 9781470468040
T3 - Contemporary Mathematics
SP - 127
EP - 133
BT - Computational Aspects of Discrete Subgroups of Lie Groups
A2 - Detinko, Alla
A2 - Kapovich, Michael
A2 - Kontorovich, Alex
A2 - Sarnak, Peter
A2 - Schwartz, Richard
PB - American Mathematical Society
T2 - Virtual Conference on Computational Aspects of Discrete Subgroups of Lie Groups, 2021
Y2 - 14 June 2021 through 18 June 2021
ER -