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Maximal representations in lattices of the symplectic group
Published 13 Jul 2023 in math.GT, math.GR, and math.NT | (2307.06791v2)
Abstract: We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k.
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