2006/08/04 by Mitya Boyarchenko, Boyarchenko, Mitya, Maria Sabitova +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories #math.RT
paper · pdf · doi:10.48550/arxiv.math/0608126
19 pages, LaTeX, all comments are welcome
arxiv created 2006/08/04 · openalex publication_date 2006/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central to the classical orbit method. Instead, Kirillov's character formula becomes the fundamental object of study. Our results are then used to produce an alternate proof of the orbit method classification of complex irreducible representations of p-groups of nilpotence class less than p, where p is a prime, and of continuous complex irreducible representations of uniformly powerful pro-p-groups (with a certain modification for p=2). As a main application, we give a quick and transparent proof of the p-adic analogue of Brown's theorem, stating that for a nilpotent Lie group over Qp the Fell topology on the set of isomorphism classes of its irreducible representations coincides with the quotient topology on the set of its coadjoint orbits.