Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

Recent Developments - Horospherically Invariant Measures and a Rank Dichotomy for Anosov Groups (2/2)

22 juin 2023, 11:00

1h

Le Bois-Marie

Orateur

Prof. Minju Lee (University of Chicago)

Description

Let $G$ be a product of simple real algebraic groups of rank one and $\mathrm{\Gamma }$ be a Zariski dense and Anosov subgroup with respect to a minimal parabolic subgroup $P$. Let $N$ be the unipotent radical of $P$. For each direction $u$ in the interior of Weyl chamber, we show that there exists at most one $N$-invariant measure in $\mathrm{\Gamma }\mathrm{\setminus }G$ which is supported on the forward recurrent subset for the $\exp (tu)$-action. This can be viewed as a generalization of the unique ergodicity result for the horospherical action due to Furstenberg, Burger, Roblin and Winter for $\mathrm{\Gamma }$ convex cocompact. This is joint work with Or Landesberg, Elon Lindenstrauss and Hee Oh.

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