3 papers
math.RT2026
Multiplicity One Property for Archimedean Theta Correspondence
Zhibin Geng, Kaidi Wu
For any archimedean reductive dual pair, we prove that the Jordan-Hölder multiplicity of the small theta lift in the full theta lift is one. The main input is an equality between t…
math.RT2026
Casselman-Wallach property for homological theta lifting
Zhibin Geng, Hang Xue
In this paper, we establish the Casselman-Wallach property for homological theta lifting over archimedean local fields. As a consequence, the Euler-Poincaré characteristic is a wel…
math.RT2025
On the existence of twisted Shalika periods: the Archimedean case
Zhibin Geng
Let $\K$ be an archimedean local field. We investigate the existence of the twisted Shalika functionals on irreducible admissible smooth representations of $\GL_{2n}(\K)$ in terms…