Unitary Shimura Correspondence for Complex Classical Groups
In this paper, we construct a lifting operator from the Grothendieck group of admissible Harish-Chandra modules of $G =\mathrm{SO}_{2n}(\mathbb C)$ (resp. $\mathrm{Sp}_{2n}(\mathbb C)$) to that of genuine representations of $\mathrm{Spin}_{2n}(\mathbb C)$ (resp. $\mathrm{Spin}_{2n+1}(\mathbb C)$). We determine the lift...