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Invariants of pairs in $ SL(4, \mathbb{C})$ and $ SU(3, 1)$


Authors: Krishnendu Gongopadhyay and Sean Lawton
Journal: Proc. Amer. Math. Soc. 145 (2017), 4703-4715
MSC (2010): Primary 14D20, 20H10; Secondary 20C15, 14L30, 20E05, 30F40, 15B57, 51M10
DOI: https://doi.org/10.1090/proc/13638
Published electronically: June 16, 2017
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Abstract: We describe a minimal global coordinate system of order 30 on the $ \textup {SL}(4,\mathbb{C})$-character variety of a rank 2 free group. Using symmetry within this system, we obtain a smaller collection of 22 coordinates subject to 5 further real relations that determine conjugation classes of generic pairs of matrices in $ \textup {SU}(3,1)$.


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Additional Information

Krishnendu Gongopadhyay
Affiliation: Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, S.A.S. Nagar, Sector 81, P. O. Manauli, Pin 140306, India
Email: krishnendug@gmail.com, krishnendu@iisermohali.ac.in

Sean Lawton
Affiliation: Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, Virginia 22030
Email: slawton3@gmu.edu

DOI: https://doi.org/10.1090/proc/13638
Keywords: Character variety, $4\times 4$ invariants, complex hyperbolic space, two-generator subgroup, traces
Received by editor(s): March 3, 2016
Received by editor(s) in revised form: December 9, 2016
Published electronically: June 16, 2017
Communicated by: Michael Wolf
Article copyright: © Copyright 2017 American Mathematical Society