C. Lecouvey

activity

20022026

most citedRandom walks in Weyl chambers and crystals

21 citations · 102 across the 49 of their papers we have counts for

collaborators

Showing math.COShow all

25 papers · 1 filter

math.CO2023

Crystal isomorphisms and Mullineux involution II

Nicolas Jacon, Cédric Lecouvey

We present a new combinatorial and conjectural algorithm for computing the Mullineux involution for the symmetric group and its Hecke algebra. This algorithm is built on a conjectu…

math.CO2023

Homology rings of affine grassmannians and positively multiplicative graphs

Jérémie Guilhot, Cédric Lecouvey, Pierre Tarrago

Let $g$ be an untwisted affine Lie algebra with associated Weyl group $W_{a}$ . To any level 0 weight $γ$ we associate a weighted graph $Γ_{γ}$ that encodes the orbit of $γ$ …

math.CO2022

Non symmetric Cauchy kernel, crystals and last passage percolation

Olga Azenhas, Thomas Gobet, Cédric Lecouvey

We use non-symmetric Cauchy kernel identities to get the law of last passagepercolation models in terms of Demazure characters. The construction is basedon some restrictions of the…

math.CO2022

Submodular functions in additive combinatorics problems for group actions and representations

Vincent Beck, Cédric Lecouvey

We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion…

math.CO2022

Basics on positively multiplicative graphs and algebras

Jérémie Guilhot, Cédric Lecouvey, Pierre Tarrago

An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $B$ with nonnegative structure constants in…

math.CO2021

Generalised Howe dualityand injectivity of induction: the symplectic case

Thomas Gerber, Jeremie Guilhot, Cédric Lecouvey

We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The fi…

math.CO2021

Towards a Combinatorial Model for $q$ -weight Multiplicities of Simple Lie Algebras (Extended Abstract)

Cédric Lecouvey, Cristian Lenart, Adam Schultze

Kostka-Foulkes polynomials are Lusztig's $q$ -analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polyno…

math.CO2020

Duality and bicrystals on infinite binary matrices

Thomas Gerber, Cédric Lecouvey

The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short…

math.CO2020

Cores of Ariki-Koike algebras

Nicolas Jacon, Cédric Lecouvey

We study a natural generalization of the notion of cores for l-partitions attached with a multi-charge s $\in$ Z^l : the (e, s)-cores. We rely them both to the combinatorics and th…

math.CO2019★ 9 cited

Keys and Demazure crystals for Kac-Moody algebras

Nicolas Jacon, Cédric Lecouvey

The Key map is an important tool in the determination of the Demazure crystals associated to Kac-Moody algebras. In finite type A, it can be computed in the tableau realization of…

math.CO2018

Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset

Cédric Lecouvey, Pierre Tarrago

We use k-Schur functions to get the minimal boundary of the k-bounded partition poset. This permits to describe the central random walks on affine Grassmannian elements of type A a…

math.CO2015

Additive combinatorics methods in associative algebras

Vincent Beck, Cédric Lecouvey

We adapt methods coming from additive combinatorics in groups to the study of linear span in associative unital algebras. In particular, we establish for these algebras analogues o…

math.CO2014

Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné

We introduce and characterize central probability distributions on Littelmann paths. Next we establish a law of large numbers and a central limit theorem for the generalized Pitman…

math.CO2013

Conditioned random walks from Kac-Moody root systems

Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné

Random paths are time continuous interpolations of random walks. By using Littelmann path model, we associate to each irreducible highest weight module of a Kac Moody algebra g a r…

math.CO2011

Plünnecke and Kneser type theorems for dimension estimates

Cédric Lecouvey

Given a division ring K containing the field k in its center and A,B two finite subsets of K\{0}, we give some analogues of Plünnecke and Kneser theorems for the dimension of the k…

math.CO2008★ 4 cited

On the product of vector spaces in a commutative field extension

Shalom Eliahou, Michel Kervaire, Cédric Lecouvey

Let $K \subset L$ be a commutative field extension. Given $K$ -subspaces $A, B$ of $L$ , we consider the subspace $< A B >$ spanned by the product set $A B = {ab ∣ a \in A, b \in B}$ .…

math.CO2008★ 10 cited

On linear versions of some addition theorems

Shalom Eliahou, Cédric Lecouvey

Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the…

math.CO2006★ 3 cited

Signed permutations and the four color theorem

Shalom Eliahou, Cedric Lecouvey

To each permutation $σ$ in $S_{n}$ we associate a triangulation of a fixed $(n + 2)$ -gon. We then determine the fibers of this association and show that they coincide with the sylves…

math.CO2006★ 1 cited

Crystal bases and combinatorics of infinite rank quantum groups

Cedric Lecouvey

The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite ro…

math.CO2005

Branching rules, Kostka-Foulkes polynomials and $q$ -multiplicities in tensor product for the root systems $B_n, C_n$ and $D_n$

Cédric Lecouvey

The Kostka-Foulkes polynomials $K$ related to a root system $ϕ$ can be defined as alternated sums running over the Weyl group associated to $ϕ .$ By restricting these sums over the…

math.CO2004★ 3 cited

Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems $B_{n}, C_{n}$ and $D_{n} .$

Cedric Lecouvey

We use Kashiwara-Nakashima's combinatorics of crystal graphs associated to the roots sytems $B_{n}$ and $D_{n}$ to extend the results of \QCITE{cite}{}{lec3} and \QCITE{cite}{}{Mor…

math.CO2003

Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_{n}$

Cedric lecouvey

We establish a Morris type recurrence formula for the root system $C_{n}$ .\ Next we introduce cyclage graphs for the corresponding Kashiwara-Nakashima's tableaux and use them to de…

math.CO2002★ 4 cited

Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$

Cedric lecouvey

We use Kashiwara's theory of crystal bases to study plactic monoids for $U_{q} (s o_{2 n + 1})$ and $U_{q} (s o_{2 n})$ . Simultaneously we describe a Schensted type correspondence in the c…

math.CO2002★ 2 cited

Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q} (G_{2})$ -module

cedric Lecouvey

We use Kang-Misra's combinatorial description of the crystal graphs for $U_{q} (G_{2})$ to introduce the plactic monoid for type $G_{2}$ . Then we describe the corresponding insertio…

Crystal isomorphisms and Mullineux involution II

Homology rings of affine grassmannians and positively multiplicative graphs

Non symmetric Cauchy kernel, crystals and last passage percolation

Submodular functions in additive combinatorics problems for group actions and representations

Basics on positively multiplicative graphs and algebras

Generalised Howe dualityand injectivity of induction: the symplectic case

Towards a Combinatorial Model for q-weight Multiplicities of Simple Lie Algebras (Extended Abstract)

Duality and bicrystals on infinite binary matrices

Cores of Ariki-Koike algebras

Keys and Demazure crystals for Kac-Moody algebras

Alcove random walks, k-Schur functions and the minimal boundary of the k-bounded partition poset

Additive combinatorics methods in associative algebras

Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

Conditioned random walks from Kac-Moody root systems

Plünnecke and Kneser type theorems for dimension estimates

On the product of vector spaces in a commutative field extension

On linear versions of some addition theorems

Signed permutations and the four color theorem

Crystal bases and combinatorics of infinite rank quantum groups

Branching rules, Kostka-Foulkes polynomials and q-multiplicities in tensor product for the root systems B_n,C_n and D_n

Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems Bn​,Cn​ and Dn​.

Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system Cn​

Schensted-type correspondences and plactic monoids for types Bn​ and Dn​

Schensted type correspondence for type G2​ and computation of the canonical basis of a finite dimensional Uq​(G2​)-module

Towards a Combinatorial Model for $q$ -weight Multiplicities of Simple Lie Algebras (Extended Abstract)

Branching rules, Kostka-Foulkes polynomials and $q$ -multiplicities in tensor product for the root systems $B_n, C_n$ and $D_n$

Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems $B_{n}, C_{n}$ and $D_{n} .$

Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system $C_{n}$

Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$

Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q} (G_{2})$ -module