Zobrazeno 1 - 10
of 158
pro vyhledávání: '"Lecouvey, Cédric"'
Autor:
Lecouvey, Cédric, Wahiche, David
We expand the affine Weyl denominator formulas as signed $q$-series of ordinary Weyl characters running over the affine Grassmannian. Here the grading in $q$ coincides with the (dual) atomic length of the root system considered as introduced by Chape
Externí odkaz:
http://arxiv.org/abs/2404.10532
Autor:
Jacon, Nicolas, Lecouvey, Cédric
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 conjectural property of crystal isomorphisms which can be rephrased in a purel
Externí odkaz:
http://arxiv.org/abs/2307.01065
Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the graph $\G
Externí odkaz:
http://arxiv.org/abs/2306.16105
Publikováno v:
Tunisian J. Math. 6 (2024) 249-297
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 RSK correspondence that we rephrase in a unifiedway which is compatib
Externí odkaz:
http://arxiv.org/abs/2212.06587
We study a class of commuting Markov kernels whose simplest element describes the movement of $k$ particles on a discrete circle of size $n$ conditioned to not intersect each other. Such Markov kernels are related to the quantum cohomology ring of th
Externí odkaz:
http://arxiv.org/abs/2211.12836
Autor:
Beck, Vincent, Lecouvey, Cédric
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 of left invariant submodular function defined on power sets which pla
Externí odkaz:
http://arxiv.org/abs/2210.08845
A graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathfrak{B}$ with nonnegative structure constants in which the matrix multiplication by $A$ coincides with $A$. The goal of this pa
Externí odkaz:
http://arxiv.org/abs/2205.08889
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 polynomials have non-negative coefficients. A statistic on semistandard Youn
Externí odkaz:
http://arxiv.org/abs/2110.15394
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 first approach allows us to establish a generalised version where weight
Externí odkaz:
http://arxiv.org/abs/2110.04029
Autor:
Gerber, Thomas, Lecouvey, Cédric
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 proof of the equality between Kostka polynomials and one-dimensional s
Externí odkaz:
http://arxiv.org/abs/2009.10397