21 citations · 102 across the 49 of their papers we have counts for
23 papers · 1 filter
Quantized Howe-type dualities via Koornwinder polynomials and the X=K phenomenon
Thomas Gerber, Bogdan Ion, Cédric Lecouvey +1
We derive the equality between one-dimensional sums associated with tensor products of Kirillov-Reshetikhin column crystals of classical affine types and Lusztig q-analogues of wei…
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…
Atomic decomposition of characters and crystals
Cedric Lecouvey, Cristian Lenart
Lascoux stated that the type A Kostka-Foulkes polynomials K_{lambda,mu}(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, the former po…
Combinatorics of generalized exponents
Cedric Lecouvey, Cristian Lenart
We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type A_{n-1}, we red…
Central measures on multiplicative graphs, representations of Lie algebras and weight polytopes
Cedric Lecouvey, Pierre Tarrago
To each finite-dimensional representation of a simple Lie algebra is associated a multiplicative graph in the sense of Kerov and Vershik definedfrom the decomposition of its tensor…
Crystal isomorphisms and wall-crossing maps for rational Cherednik algebras
Nicolas Jacon, Cédric Lecouvey
We show that the wall crossing bijections between simples of the category O of the rational Cherednik algebras reduce to particular crystal isomorphisms which can be computed by a…
Springer basic sets and modular Springer correspondence for classical types
Daniel Juteau, Cédric Lecouvey, Karine Sorlin
We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and w…
Isomorphic induced modules and Dynkin diagram automorphisms of semisimple Lie algebras
Jérémie Guilhot, Cédric Lecouvey
Consider a simple Lie algebra and a Levi subalgebra. Two irreducible $\overline{% \mathfrak{g}}$-modules yield isomor…
Conditioned one-way simple random walk and representation theory
Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné
We call one-way simple random walk a random walk in the quadrant Z_+^n whose increments belong to the canonical base. In relation with representation theory of Lie algebras and sup…
A combinatorial decomposition of higher level Fock spaces
Nicolas Jacon, Cédric Lecouvey
We give a simple characterization of the highest weight vertices in the crystal graph of the level l Fock spaces. This characterization is based on the notion of totally periodic s…
Random walks in Weyl chambers and crystals
Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné
We use Kashiwara crystal basis theory to associate a random walk W to each irreducible representation V of a simple Lie algebra. This is achieved by endowing the crystal attached t…
The modular branching rule for affine Hecke algebras of type A
Susumu Ariki, Nicolas Jacon, Cédric Lecouvey
For the affine Hecke algebra of type A at roots of unity, we make explicit the correspondence between geometrically constructed simple modules and combinatorially constructed simpl…
Factorization of the canonical bases for higher level Fock spaces
Susumu Ariki, Nicolas Jacon, Cédric Lecouvey
The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition mat…
Kashiwara and Zelevinsky involutions in affine type A
Nicolas Jacon, Cédric Lecouvey
We first describe how the Kashiwara involution on crystals of affine type is encoded by the combinatorics of aperiodic multisegments. This yields a simple relation between this…
The modular branching rule for affine Hecke algebras of type A
Susumu Ariki, Nicolas Jacon, Cédric Lecouvey
For the affine Hecke algebra of type A at roots of unity, we make explicit the correspondence between geometrically constructed simple modules and combinatorially constructed simpl…
On the Mullineux involution for Ariki-Koike algebras
Nicolas Jacon, Cédric Lecouvey
This note is concerned with a natural generalization of the Mullineux involution for Ariki-Koike algebras. Using a result of Fayers together with previous results by the authors, w…
On q-analogs of weight multiplicities for the Lie superalgebras gl(n,m) and spo(2n,M)
Cedric Lecouvey, Cristian Lenart
The paper is devoted to the generalization of Lusztig's q-analog of weight multiplicities to the Lie superalgebras gl(n,m) and spo(2n,M). We define such q-analogs K_{lambda,mu}(q)…
Crystal isomorphisms for irreducible highest weight U_{v}{\hat{sl}}_{e})-modules of higher level
Nicolas Jacon, Cédric Lecouvey
We study the crystal graphs of irreducible $U_{v}(\hat{sl}}_{e})$-modules of higher level l. Generalizing works of the first author, we obtain a simple description of the bijection…
Stabilized plethysms for the classical Lie groups
Cedric Lecouvey
The plethysms of the Weyl characters associated to a classical Lie group by the symmetric functions stabilize in large rank. In the case of a power sum plethysm, we prove that the…
Universal graded characters and limit of Lusztig -analogues
Cedric Lecouvey
Let G be a symplectic or orthogonal complex Lie group with Lie algebra g. As a G-module, the decomposition of the symmetric algebra S(g) into its irreducible components can be expl…
Parabolic Kazhdan-Lusztig polynomials, plethysm and gereralized Hall-Littlewood functions for classical types
Cedric Lecouvey
We use power sums plethysm operators to introduce H functions which interpolate between the Weyl characters and the Hall-Littlewood functions Q' corresponding to classical Lie grou…
Quantization of branching coefficients for classical Lie groups
Cedric lecouvey
We study natural quantizations of branching coefficients corresponding to the restrictions of the classical Lie groups to their Levi subgroups. We show that they admit a stable lim…
A duality between -multiplicities in tensor products and -multiplicities of weights for the root systems or
Cedric Lecouvey
Starting from Jacobi-Trudi's type determinental expressions for the Schur functions corresponding to types and we define a natural -analogue of the multiplicity $[V(λ…