Symmetric powers of Nat SL(2,K)

2015/05/01 by Adrien Deloro, Deloro, Adrien
Mathematics · #20C07 #20G05 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1505.00163

openalex publication_date 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We identify the representations \mathbbK[X^k, X^k-1Y, …, Y^k] among abstract ℤ[SL₂(\mathbbK)]-modules. One result is on ℚ[SL₂(ℤ)]-modules of short nilpotence length and generalises a classical "quadratic" theorem by Smith and Timmesfeld. Another one is on extending the linear structure on the module from the prime field to \mathbbK. All proofs are by computation in the group ring using the Steinberg relations.

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