On the local Langlands correspondence and Arthur conjecture for even orthogonal groups. (English) Zbl 1419.11088
Summary: In this paper, we highlight and state precisely the local Langlands correspondence for quasi-split \( \mathrm {O}_{2n}\) established by Arthur. We give two applications: Prasad’s conjecture and Gross-Prasad conjecture for \( \mathrm {O}_n\). Also, we discuss the Arthur conjecture for \( \mathrm {O}_{2n}\), and establish the Arthur multiplicity formula for \( \mathrm {O}_{2n}\).
MSC:
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 11F55 | Other groups and their modular and automorphic forms (several variables) |
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