Work

PARITY OF CONJUGATE SELF-DUAL REPRESENTATIONS OF INNER FORMS OF $\operatorname { {GL}}_n$ OVER p-ADIC FIELDS

Year: 2024

Type: article

Abstract: We prove a general formula that relates the parity of the Langlands parameter of a conjugate self-dual discrete series representation of $\operatorname { {GL}}_n$ to the parity of its Jacquet-Langlands image. It gives a generalization of a partial result by Mieda concerning the case of invariant $1/n$ and supercuspidal representations. It also gives a variation of the result on the self-dual case by Prasad and Ramakrishnan.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748024000240

Author: Yugo Takanashi

Institution: The University of Tokyo

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Japan Society for the Promotion of Science