Explicit Plancherel Formula for the Space of Symplectic Forms

Author:

Lapid Erez1,Offen Omer2

Affiliation:

1. Department of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel

2. Department of Mathematics, Brandeis University, 4 South Street, Waltham, MA 02453, USA

Abstract

Abstract We provide a Plancherel decomposition for the space of symplectic bilinear forms of rank $2n$ over a local non-Archimedean field $F$ in terms of that of $\operatorname{GL}_n(F)$.

Funder

ISF

BSF

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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3. P-invariant distributions on GL (N) and the classification of unitary representations of GL (N) (non-Archimedean case);Bernstein,1984

4. Plancherel formula for $G{L}_n(F)\setminus G{L}_n(E)$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups;Beuzart-Plessis,2018

5. Representations of the group $\textrm{GL}\left (\textrm{n},\textrm{F}\right ),$ where $\textrm{F}$ is a local non-Archimedean field;Bernšteĭn;Uspehi Mat. Nauk,1976

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