Local rigidity of complex hyperbolic lattices in semisimple Lie groups

TL;DR

This paper proves the local rigidity of complex hyperbolic lattices within certain classical Hermitian semisimple Lie groups, extending and generalizing previous results in the field.

Contribution

It establishes the local rigidity of complex hyperbolic lattices in multiple classical Hermitian semisimple Lie groups, broadening the scope of earlier findings.

Findings

Proves local rigidity for lattices in $SU(np,p)$, $Sp(2n+2, ext{R})$, $SO^*(2n+2)$, and $SO(2n,2)$.

Generalizes previous results by extending the class of groups where rigidity holds.

Reproves or extends results from prior works such as extbackslash cite exttt{GM, KKP, Klingler-inv, Pozzetti}.

Abstract

We show the local rigidity of complex hyperbolic lattices in classical Hermitian semisimple Lie groups, $SU(np,p), Sp(2n+2,\mathbb R), SO^*(2n+2), SO(2n,2)$. This reproves or generalizes some results in \cite{GM, KKP, Klingler-inv, Pozzetti}.