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Article Dans Une Revue Journal of Group Theory Année : 2016

Symmetric powers of Nat SL(2,K)

Résumé

In this paper, we identify the representations ${\mathbb{K}[X^{k},X^{k-1}Y,\dots,Y^{k}]}$ among abstract ${\mathbb{Z}[\operatorname{SL}_{2}(\mathbb{K})]}$ -modules. One result is on ${\mathbb{Q}[\operatorname{SL}_{2}(\mathbb{Z})]}$ -modules of nilpotence length at most 5 and generalises a classical "quadratic" theorem by Smith and Timmesfeld; there are reasons to believe that this generalisation is close to optimal. Another result is on extending the linear structure on the module from the prime field to ${\mathbb{K}}$ . All proofs are by computation in the group ring using the Steinberg relations.
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Dates et versions

hal-04282066 , version 1 (13-11-2023)

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Adrien Deloro. Symmetric powers of Nat SL(2,K). Journal of Group Theory, 2016, 19 (4), pp.661-692. ⟨10.1515/jgth-2015-0049⟩. ⟨hal-04282066⟩
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