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arXiv · 2204.08830

Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields

Yugo Takanashi
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Abstract

We prove a general formula that relates the parity of the Langlands parameter of a conjugate self-dual discrete series representation of $\mathrm{GL}_n$ 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.

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Yugo Takanashi. 2022-04-19. Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields. https://doi.org/10.1017/s1474748024000240

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