Invariants of pairs in 𝑆𝐿(4,ℂ) and 𝕊𝕌(3,1)

Gongopadhyay, Krishnendu; Lawton, Sean

doi:10.1090/proc/13638

Invariants of pairs in $\mathrm {SL}(4, \mathbb {C})$ and $\mathrm {SU}(3, 1)$
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Proc. Amer. Math. Soc. 145 (2017), 4703-4715 Request permission

Abstract:

We describe a minimal global coordinate system of order 30 on the $\mathrm {SL}(4,\mathbb {C})$-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 $\mathrm {SU}(3,1)$.

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