The Langlands dual and unitary dual of quasi-split 𝑃𝐺𝑆𝑂₈^{𝐸}

Author:

Luo Caihua

Abstract

This paper serves two purposes, by adopting the classical Casselman–Tadi c ´ \acute {c} ’s Jacquet module machine and the profound Langlands–Shahidi theory, we first determine the explicit Langlands classification for quasi-split groups P G S O 8 E PGSO^E_8 which provides a concrete example to guess the internal structures of parabolic inductions. Based on the classification, we further sort out the unitary dual of P G S O 8 E PGSO^E_8 and compute the Aubert duality which could shed light on the final answer of Arthur’s conjecture for P G S O 8 E PGSO_8^E . As an essential input to obtain a complete unitary dual, we also need to determine the local poles of triple product L-functions which is done in the appendix. As a byproduct of the explicit unitary dual, we verified Clozel’s finiteness conjecture of special exponents and Bernstein’s unitarity conjecture concerning AZSS duality for P G S O 8 E PGSO_8^E .

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

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