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arXiv · 2310.00735

Twisted Jacquet modules: a conjecture of D. Prasad

Santosh Nadimpalli·Mihir Sheth
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Abstract

In this note, we study the twisted Jacquet modules of sub-quotients of principal series representations of ${\rm GL}_2(D)$ where $D$ is a division algebra over a non-archimedean local field $F$. We begin with a proof of a conjecture due to D. Prasad on twisted Jacquet modules of Speh representations of ${\rm GL}_2(D)$ when $D$ is the quaternionic division algebra. Later, when $D$ is an arbitrary division algebra over $F$, we focus on depth-zero principal series and compute the dimensions of twisted Jacquet modules of generalised Speh representations and investigate their structure explicitly.

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BibTeXRIS

Santosh Nadimpalli, Mihir Sheth. 2023-10-01. Twisted Jacquet modules: a conjecture of D. Prasad. https://arxiv.org/abs/2310.00735

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