arXiv subjects
Publications and source records attributed to Zhibin Geng.
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 well-defined element in the Grothendieck group of Casselman-Wallach representations. Our main tool is a corank-one parabolic stable filtration on the Weil representation.
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 of their L-parameters. As part of our proof, we establish a Hochschild-Serre spectral sequence for nilpotent normal subgroups and a Kunneth formula in the framework of Schwartz homology. We also prove the analogous result for twisted linear periods using theta correspondence. The existence of twisted Shalika functionals on representations of $\GL_{2n}^{+}(\R)$ is also studied, which is of independent interest.