'Alvaro Guti'errez

activity

20242026

collaborators

10 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.CO2026

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…

math.CO2025

A geometric and generating function approach to plethysm

Álvaro Gutiérrez, Rosa Orellana, Franco Saliola +2

Plethysm coefficients $a_{μ [ν]}^{λ}$ are the structure coefficients of the plethysm of Schur functions $s_{μ} [s_{ν}] = \sum_{λ} a_{μ [ν]}^{λ} s_{λ}$ . We study a bivariate gener…

math.CO2025

Schur log-concavity and the quantum Pascal triangle

Álvaro Gutiérrez, Christian Krattenthaler

We say a sequence $f_{0}, f_{1}, f_{2}, \dots$ of symmetric functions is Schur log-concave if $f_{n}^{2} - f_{n - 1} f_{n + 1}$ is Schur positive for all $n \geq 1$ . We conjecture that a very gener…

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

On the generalised Foulkes conjecture for $SL_{2} (C)$ under divisibility conditions

Moritz Gangl, Álvaro Gutiérrez, Michał Szwej

The generalised Foulkes conjecture for $SL_{2} (C)$ was recently proved under mild divisibility conditions by Raicu, Sam, Weyman, and Yang, who showed surjectivity o…

math.PR2024

Weak lumping of left-invariant random walks on left cosets of finite groups

Edward Crane, Álvaro Gutiérrez, Erin Russell +1

Let $G$ be a finite group and let $H$ be a subgroup of $G$ . The left-invariant random walk driven by a probability measure $w$ on $G$ is the Markov chain in which from any state $x…

math.CO2024

Towards plethystic $sl_{2}$ crystals

Álvaro Gutiérrez

To find crystals of $sl_{2}$ representations of the form $Λ^{n} Sym^{r} C^{2}$ it suffices to solve the combinatorial problem of decomposing Young's lattice into s…

math.CO2024

Principal minors of the distance matrix of a tree

Álvaro Gutiérrez, Adrián Lillo

Let $T = ([n], E)$ be a tree and let $D = (d (i, j))_{i, j \leq n}$ be the distance matrix of $T$ . Let $S \subseteq [n]$ . We give the first combinatorial proof for a formula to compu…

math.CO2024

Non-intersecting paths and the determinant of the distance matrix of a tree

Emmanuel Briand, Luis Esquivias-Quintero, Álvaro Gutiérrez +2

We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel-…

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

More minor summation formulae

A geometric and generating function approach to plethysm

Schur log-concavity and the quantum Pascal triangle

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

On the generalised Foulkes conjecture for SL2​(C) under divisibility conditions

Weak lumping of left-invariant random walks on left cosets of finite groups

Towards plethystic sl2​ crystals

Principal minors of the distance matrix of a tree

Non-intersecting paths and the determinant of the distance matrix of a tree

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

On the generalised Foulkes conjecture for $SL_{2} (C)$ under divisibility conditions

Towards plethystic $sl_{2}$ crystals