For locally algebraic integral weights, the Bernstein-Zelevinsky dual of a locally analytic principal series representation equals another locally analytic principal series built from the dual Verma module and the smooth dual of the character.
Extending meromorphic connections to coadmissible D -modules
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Bernstein-Zelevinsky duality for locally analytic principal series representations
For locally algebraic integral weights, the Bernstein-Zelevinsky dual of a locally analytic principal series representation equals another locally analytic principal series built from the dual Verma module and the smooth dual of the character.