Deligne categories as limits in rank and characteristic

2016/01/13 by Nate Harman, Harman, Nate · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1601.03426

openalex publication_date 2016/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give new interpretations of the Deligne categories \underlineRep(GL_t) and \underlineRep(S_t) (and their abelian envelopes) over ℂ in terms of modular representations of general linear and symmetric groups of large rank in large characteristic. In particular we make sense of the sentence "\underlineRep(S_n) is the limit of Rep(S_p+n) over \mathbbF_p as p goes to infinity". We then give examples of how to pass results between these different settings.

Citations

• Simple commutative algebras in Deligne's categories Rep(S_t)
• Stability and periodicity in the modular representation theory of\n symmetric groups

Cited by

• Classification of simple commutative algebras in the Delannoy category

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• Deligne categories and representations of the infinite symmetric group
• Deligne categories and representations of the finite general linear group, part 1: universal property
• An Introduction to Deligne Categories
• Ideals in Deligne's category Rep(GL_δ)
• Simple commutative algebras in Deligne's categories Rep(S_t)