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PARITY OF CONJUGATE SELF-DUAL REPRESENTATIONS OF INNER FORMS OF
$\operatorname { {GL}}_n$ OVER p-ADIC FIELDS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 24 / Issue 1 / January 2025
- Published online by Cambridge University Press:
- 20 September 2024, pp. 249-271
- Print publication:
- January 2025
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- Article
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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.
