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An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
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An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
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The Weyl modules are the standard modules for the Schur algebra. Their duals (the costandard modules) have well-known constructions as quotients of exterior powers and as submodules of symmetric powers. This paper presents analogous constructions for the Weyl modules themselves, introducing relations that are a non-trivial dualisation of the Garnir relations. More generally, our constructions describe endofunctors on the category of representations of any group.
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Cited by 1 Pith paper
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A field-independent filtration of plethystic modules for $\mathrm{SL}_2(\mathbb{F})$ that categorifies a product rule for the Cartan subalgebra of $\mathcal{U}_q(\mathfrak{sl}_2)$
A field-independent filtration of Δ^{(n,m)} Sym^d E with layers Sym^{n+m} Sym^{d-k} E ⊗ Δ^{(n-k,m-k)} Sym^k E categorifies the Cartan product rule of U_q(sl_2).
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