M. Wildon

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20242026

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math.RT2026

A field-independent filtration of plethystic modules for $SL_{2} (F)$ that categorifies a product rule for the Cartan subalgebra of $U_{q} (sl_{2})$

Ãlvaro GutiÃ©rrez, Ãlvaro L. MartÃnez, MichaÅ Szwej +1

We lift a product rule in the Cartan subalgebra of quantum $sl_{2}$ to a filtration of the plethystic representation $I^^{(n, m)} Sym^{d} E$ of the affine group schem…

math.RT2026

Modular isomorphisms of $SL_{2} (F)$ -plethysms for Weyl modules labelled by hook partitions

Ãlvaro GutiÃ©rrez, Ãlvaro L. MartÃnez, MichaÅ Szwej +1

Let $I^^{I^} »$ be the Weyl functor for the partition $I^»$ and let $E$ be the natural $2$ -dimensional representation of $SL_{2} (F)$ , where $F$ is an arbitrary…

math.RT2024

The partition algebra and the plethysm coefficients II: ramified plethysm

Chris Bowman, Rowena Paget, Mark Wildon

The plethysm coefficient $p (I^½, I^¼, I^»)$ is the multiplicity of the Schur function $s_{I^} »$ in the plethysm product $s_{I^} ½ \circ s_{I^} ¼$ . In this paper we use Schur--Weyl duality between…

math.RT2024

A new modular plethystic $SL_{2} (F)$ -isomorphism $Sym^{N - 1} E \otimes ⋀^{N + 1} Sym^{d + 1} E ≅ I^^{(2, 1^{N - 1})} Sym^{d} E$

Alvaro L. Martinez, Mark Wildon

Let $F$ be a field and let $E$ be the natural representation of $SL_{2} (F)$ . Given a vector space $V$ , let $I^^{(2, 1^{N - 1})} V$ be the kernel of the multipl…

A field-independent filtration of plethystic modules for SL2​(F) that categorifies a product rule for the Cartan subalgebra of Uq​(sl2​)

Modular isomorphisms of SL2​(F)-plethysms for Weyl modules labelled by hook partitions

The partition algebra and the plethysm coefficients II: ramified plethysm

A new modular plethystic SL2​(F)-isomorphism SymN−1E⊗⋀N+1Symd+1E≅I^(2,1N−1)SymdE

A field-independent filtration of plethystic modules for $SL_{2} (F)$ that categorifies a product rule for the Cartan subalgebra of $U_{q} (sl_{2})$

Modular isomorphisms of $SL_{2} (F)$ -plethysms for Weyl modules labelled by hook partitions

A new modular plethystic $SL_{2} (F)$ -isomorphism $Sym^{N - 1} E \otimes ⋀^{N + 1} Sym^{d + 1} E ≅ I^^{(2, 1^{N - 1})} Sym^{d} E$