The Metaplectic Representation is Faithful

2024/01/09 by Christopher Chang, Chang, Christopher, Simeon Hellsten +5
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.04581

Abstract

We develop methods to show that infinite-dimensional modules over the Iwasawa algebra KG of a uniform pro-p group are faithful and apply them to show that the metaplectic representation for the symplectic group is faithful.

Related

• K₀-invariance of the completely faithful property of Iwasawa modules
• The mod-p representation theory of the metaplectic cover of GL₂(Q_p)
• Local metaplectic correspondence and applications
• Restriction of the metaplectic representation over a p-adic field to an anisotropic torus
• Generic representations of metaplectic groups and their theta lifts