On the restriction of some irreducible mod p representations

2024/05/30 by Shubhanshi Gupta, Gupta, Shubhanshi · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.20007

openalex publication_date 2024/05/30 · openalex created_date 2024/06/01 · openalex updated_date 2026/07/28

Abstract

For a prime p, let \mathbbF_q be a finite extension of \mathbbF_p. The restriction of an irreducible mod p representation of GL₂(\mathbbF_q) to its subgroup GL₂(\mathbbF_p) can be seen as a tensor product of irreducible representations of GL₂(\mathbbF_p). In this paper, we study the restriction of some of these representations of GL₂(\mathbbF_q) to GL₂(\mathbbF_p), for q=p² and p³ using elementary tools and give explicit socle filtration when q=4. We prove that when q=p², a special class of representations of GL₂(\mathbbF_q) are distinguished by suitable characters of GL₂(\mathbbF_p).

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• Restriction problem for mod p representations of GL₂ over a finite field

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