Explicit Plancherel formula for the space of symplectic forms

TL;DR

This paper derives an explicit Plancherel formula for the space of symplectic bilinear forms over a local non-archimedean field, linking it to the representation theory of GL(n).

Contribution

It provides the first explicit Plancherel decomposition for symplectic forms, connecting it to the well-understood case of GL(n).

Findings

Explicit Plancherel formula for symplectic forms space.

Decomposition expressed via GL(n) representations.

Advances harmonic analysis on symplectic spaces.

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 $GL_n(F)$.