Michal Szwej

collaborators

3 papers

math.RT2026

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

Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1

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

math.RT2025

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

Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1

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

math.CO2025

A new bijective proof of the $q$ -Pfaff--Saalschütz identity with applications to quantum groups

Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1

We present a combinatorial proof of the $q$ -Pfaff--Saalschütz identity by a composition of explicit bijections, in which $q$ -binomial coefficients are interpreted as counting subsp…

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

A new bijective proof of the q-Pfaff--Saalschütz identity with applications to quantum groups

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 bijective proof of the $q$ -Pfaff--Saalschütz identity with applications to quantum groups