Generic Representation Theory of the Heisenberg Group

2011/05/25 by Michael Crumley, Crumley, Michael
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1105.4926

arxiv created 2011/05/25 · openalex publication_date 2011/05/25 · arxiv updated 2011/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we extend a result for representations of the Additive group G_a given in [3] to the Heisenberg group H₁. Namely, if p is greater than 2d then all d-dimensional characteristic p representations for H₁ can be factored into commuting products of representations, with each factor arising from a representation of the Lie algebra of H₁, one for each of the the representation's Frobenius layers. In this sense, for a fixed dimension and large enough p, all representations for H₁ look generically like representations for direct powers of it over a field of characteristic zero. The reader may consult chapter 13 of [1] for a fuller account of what follows.

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