10 papers
A field-independent filtration of plethystic modules for that categorifies a product rule for the Cartan subalgebra of
Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1
We lift a product rule in the Cartan subalgebra of quantum to a filtration of the plethystic representation of the affine group scheme…
More minor summation formulae
Shane Chern, Theresia Eisenkölbl, Ilse Fischer +8
We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. The…
A geometric and generating function approach to plethysm
Álvaro Gutiérrez, Rosa Orellana, Franco Saliola +2
Plethysm coefficients are the structure coefficients of the plethysm of Schur functions . We study a bivariate gener…
Schur log-concavity and the quantum Pascal triangle
Álvaro Gutiérrez, Christian Krattenthaler
We say a sequence of symmetric functions is Schur log-concave if is Schur positive for all . We conjecture that a very gener…
Modular isomorphisms of -plethysms for Weyl modules labelled by hook partitions
Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1
Let be the Weyl functor for the partition and let be the natural -dimensional representation of , where is an arbitrary fie…
On the generalised Foulkes conjecture for under divisibility conditions
Moritz Gangl, Álvaro Gutiérrez, Michał Szwej
The generalised Foulkes conjecture for was recently proved under mild divisibility conditions by Raicu, Sam, Weyman, and Yang, who showed surjectivity o…