Maximal representations of surface groups in bounded symmetric domains
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- by Luis Hernández PDF
- Trans. Amer. Math. Soc. 324 (1991), 405-420 Request permission
Abstract:
Let $\Gamma$ be the fundamental group of a hyperbolic surface of genus $g$; for $1 \le p \le q,PSU(p,q)$ is the group of isometries of a certain Hermitian symmetric space ${D_{p,q}}$ of rank $p$. There exists a characteristic number $c:\operatorname {Hom} (\Gamma ,PSU(p,q)) \to \mathbb {R}$, which is constant on each connected component and such that $|c(\rho )| \leq 4p\pi (g - 1)$ for every representation $\rho$. We show that representations with maximal characteristic number (plus some nondegeneracy condition if $p > 2$ leave invariant a totally geodesic subspace of ${D_{p,q}}$ isometric to ${D_{p,p}}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 324 (1991), 405-420
- MSC: Primary 32M15; Secondary 22E40
- DOI: https://doi.org/10.1090/S0002-9947-1991-1033234-5
- MathSciNet review: 1033234