Classifies isomorphisms ∇^λ Sym^ℓ E ≅ ∇^μ Sym^m E for SL2(C) when partitions are conjugate or rectangular, gives complete results for two-row/column or hook shapes and partial when ℓ=m, and determines all irreducibility cases via skew partition results.
The uniqueness of plethystic factorisation
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abstract
We prove that a plethysm product of two Schur functions can be factorised uniquely and classify homogeneous and indecomposable plethysm products.
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math.RT 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Plethysms of symmetric functions and representations of $\mathrm{SL}_2(\mathbb{C})$
Classifies isomorphisms ∇^λ Sym^ℓ E ≅ ∇^μ Sym^m E for SL2(C) when partitions are conjugate or rectangular, gives complete results for two-row/column or hook shapes and partial when ℓ=m, and determines all irreducibility cases via skew partition results.