Groups from class 2 algebras and the Weil character

TL;DR

This paper studies how the Weil character of the symplectic group decomposes when restricted to certain subgroups derived from class 2 algebras, providing explicit descriptions of these decompositions.

Contribution

It offers new explicit descriptions of the Weil character restriction to specific subgroups related to class 2 algebras in symplectic groups.

Findings

Decomposition of Weil character on unipotent radical described

Restriction to centralizer explicitly characterized

Results enhance understanding of symplectic group representations

Abstract

We investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit descriptions of the decomposition of the Weil character when restricted to the unipotent radical of the stabilizer of a maximal totally isotropic subspace and to its centralizer.