Nathan Chapelier‐Laget

activity

20182026

most citedABHY Associahedra and Newton polytopes of

F

-polynomials for finite type cluster algebras

7 citations · 15 across the 13 of their papers we have counts for

collaborators

16 papers

math.CO2026

$J$ -ascent sets in parabolic quotients of Coxeter groups

Nathan Chapelier-Laget

Let $(W, S)$ be a Coxeter system and let $J \subseteq S$ . The right $J$ -ascent set $A_{R}^{J} (w) = {s \in S ∣ w s \in^{J} W, ℓ (w s) = ℓ (w) + 1}$ is a natural refinement of the classi…

math.RT2026

Entropy of affine permutations and universality of affine atomic lengths

Nathan Chapelier-Laget, Thomas Gerber, Nicolas Jacon +1

We introduce and study the notion of entropy of affine permutations and prove that it coincides with the atomic length associated with the sum of the fundamental weights for a type…

math.CO2024

A counterexample to a Brenti-Carnevale conjecture

Nathan Chapelier-Laget, Jean Fromentin

Recently, F. Brenti put a preprint on the arXiv with several interesting open problems on Coxeter groups and unimodality. In this note, we refute one of these conjectures with a co…

math.RT2024

The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $A ~_{n}$

Nathan Chapelier-Laget, Jérémie Guilhot, Eloise Little +1

The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type $A$ . To do so, we construct a balanced system of cell modules,…

math.CO2024

Generalised core partitions and Diophantine equations

Olivier Brunat, Nathan Chapelier-Laget, Thomas Gerber

We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense…

math.RT2023

Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups

Nathan Chapelier-Laget, Thomas Gobet

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_{L}^{θ}$ , where $x$ is an element of $W$ and $W_{L}^{θ}$ the subgroup of fixed points o…

math.CO2023

Low elements in dominant Shi regions

Nathan Chapelier-Laget

This note is a complement of a recent paper about low elements in affine Coxeter groups. We explain in terms of ad-nilpotent ideals of a Borel subalgebra why the minimal elements o…

math.RT2022

Atomic length on Weyl groups

Nathan Chapelier-Laget, Thomas Gerber

We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of pr…

math.CO2022

Orientation of alcoves in affine Weyl groups

Nathan Chapelier-Laget

Let $W$ be an irreducible Weyl group and $W_{a}$ its affine Weyl group. In a previous work the author introduced an affine variety $X_{W_{a}}$ , called the Shi variety of $W_a…

math.CO2022★ 2 cited

Shi arrangements and low elements in affine Coxeter groups

Nathan Chapelier-Laget, Christophe Hohlweg

Given an affine Coxeter group $W$ , the corresponding Shi arrangement is a refinement of the corresponding Coxeter hyperplane arrangements that was introduced by Shi to study Kazhda…

math.CO2021

Lattice associated to a Shi variety

Nathan Chapelier-Laget

Let $W$ be a irreducible Weyl group and $W_{a}$ its affine Weyl group. In a previous article the author defined an affine variety $X_{W_{a}}$ , called the Shi variety of $W_{a}$ …

math.CO2021

Affine twisted length function

Nathan Chapelier-Laget

Let $W_{a}$ be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements $w \in W_{a}$ in terms of $Φ^{+}$ -tuples $(k (w, α))_{α \in Φ^{+}}$ called the Shi vectors. Us…

math.CO2020

An order on circular permutations

Antoine Abram, Nathan Chapelier-Laget, Christophe Reutenauer

Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_{n}$ (that is, $n$ -cycles). It is isomorphic…

math.CO2020★ 2 cited

A symmetric group action on the irreducible components of the Shi variety associated to $W (A_{n})$

Nathan Chapelier-Laget

Let $W_{a}$ be an affine Weyl group with corresponding finite root system $Φ$ . In \cite{JYS1} Jian-Yi Shi characterized each element $w \in W_{a}$ by a $Φ^{+}$ -tuple of integers $(k(w,α…

math.CO2020★ 4 cited

Shi variety corresponding to an affine Weyl group

Nathan Chapelier-Laget

Let $W$ be an irreducible Weyl group and $W_{a}$ its affine Weyl group. In this article we show that there exists a bijection between $W_{a}$ and the integral points of an affine varie…

math.RT2018★ 7 cited

ABHY Associahedra and Newton polytopes of $F$ -polynomials for finite type cluster algebras

Véronique Bazier-Matte, Nathan Chapelier-Laget, Guillaume Douville +3

A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their constructio…

J-ascent sets in parabolic quotients of Coxeter groups

Entropy of affine permutations and universality of affine atomic lengths

A counterexample to a Brenti-Carnevale conjecture

The asymptotic Plancherel formula and Lusztig's asymptotic algebra for A~n​

Generalised core partitions and Diophantine equations

Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups

Low elements in dominant Shi regions

Atomic length on Weyl groups

Orientation of alcoves in affine Weyl groups

Shi arrangements and low elements in affine Coxeter groups

Lattice associated to a Shi variety

Affine twisted length function

An order on circular permutations

A symmetric group action on the irreducible components of the Shi variety associated to W(An​)

Shi variety corresponding to an affine Weyl group

ABHY Associahedra and Newton polytopes of F-polynomials for finite type cluster algebras

$J$ -ascent sets in parabolic quotients of Coxeter groups

The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $A ~_{n}$

A symmetric group action on the irreducible components of the Shi variety associated to $W (A_{n})$

ABHY Associahedra and Newton polytopes of $F$ -polynomials for finite type cluster algebras