Character ratios, representation varieties and random generation of finite groups of Lie type

Martin W. Liebeck, Aner Shalev, Pham Huu Tiep*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.

Original languageAmerican English
Article number107386
JournalAdvances in Mathematics
Volume374
DOIs
StatePublished - 18 Nov 2020

Bibliographical note

Funding Information:
The first and second authors acknowledge the support of EPSRC grant EP/H018891/1. The second author acknowledges the support of ERC advanced grant 247034, ISF grants 1117/13 and 686/17, BSF grant 2016072, and the Vinik chair of mathematics which he holds. The third author was partially supported by the NSF grant DMS-1839351 and DMS-1840702, the Simons Foundation Fellowship 305247, the EPSRC, the Mathematisches Forschungsinstitut Oberwolfach, and the Joshua Barlaz Chair in Mathematics. Parts of the paper were written while the third author visited the Departments of Mathematics of Imperial College London, and University of Chicago. It is a pleasure to thank Imperial College, Prof. Ngo Bao Chau, and the University of Chicago for generous hospitality and stimulating environment. The authors are grateful to the referee for insightful comments on the paper.

Funding Information:
The first and second authors acknowledge the support of EPSRC grant EP/H018891/1 . The second author acknowledges the support of ERC advanced grant 247034 , ISF grants 1117/13 and 686/17 , BSF grant 2016072 , and the Vinik chair of mathematics which he holds. The third author was partially supported by the NSF grant DMS-1839351 and DMS-1840702 , the Simons Foundation Fellowship 305247 , the EPSRC , the Mathematisches Forschungsinstitut Oberwolfach , and the Joshua Barlaz Chair in Mathematics . Parts of the paper were written while the third author visited the Departments of Mathematics of Imperial College London, and University of Chicago. It is a pleasure to thank Imperial College, Prof. Ngo Bao Chau, and the University of Chicago for generous hospitality and stimulating environment. The authors are grateful to the referee for insightful comments on the paper.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

  • Fuchsian groups
  • Random generation
  • Representation varieties

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