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Riccardo Biagioli
Frédéric Jouhet
Jiang Zeng

Institut Camille Jordan
Université Claude Bernard Lyon 1


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64th Séminaire Lotharingien de Combinatoire

March 28-31, 2010

Institut Camille Jordan - Bâtiment Braconnier
Université Claude Bernard Lyon 1
43, Bd du 11 novembre 1918
69622 Villeurbanne - France

The invited speakers of this session will be: 

Alain Lascoux (CNRS - Université Marne la Vallée, France)
Key polynomials (Demazure characters) for type A,B,C,D

Demazure characters (key polynomials) are linear bases of the ring of (Laurent) polynomials in x1,..., xn. They are defined as all possible images of dominant monomials under products of divided differences for type A,B,C,D. For example, for the type A, one has two families of operators πi and ∑i (i=1,..., n-1), which commute with the multiplication by symmetric functions in xi, xi+1, and are defined by the rules:
     πi sends 1 ---> 1 and xi+1 ---> 0, 
     ∑i sends 1 ---> 0 and xi+1 ---> -xi+1

It is remarkable that such simple tools suffice to generate interesting polynomials, which contain as a subfamily the Schur (symplectic-Schur, orthogonal-Schur) functions and verify similar properties: Cauchy kernels, adjoint bases, Pieri formulas. In type A, vexillary key polynomials and vexillary Schubert polynomials coincide. Still for this type, one can give a description of key polynomials in terms of Young tableaux satisfying flag conditions.
The talks relying on great part on the article of Amy Fu and al., Non symmetric Cauchy kernels for the classical Groups, JCTA 116 (2009) 903--917.

Arun Ram (University of Melbourne, Australia)
Lyndon words, MV polytopes and the Littelmann path model

Lecture 1Quantum groups and Lyndon words
This lecture will be a survey of the foundational work of Leclerc (following Rosso and Green) who introduced Lyndon words into the canonical basis theory and predicted the existence of the recently defined Khovanov-Lauda-Rouquier graded quiver algebras.

Lecture 2Graded quiver algebras and their representations
This talk will be a survey of the recently defined Khovanov-Lauda-Rouquier graded Hecke algebras, the role of quantum groups and Lyndon words in the combinatorial representation theory of these algebras.

Lecture 3:  Indexings of canonical bases:  Lyndon words, MV polytopes and the path model
This talk will provide a comparison of three natural indexings of canonical bases in quantum groups: indexings by products of Lyndon words,  indexing by MV polytopes, and the Littelmann path (alcove walk) indexings. The path model indexings can be viewed as generalizations of Young tableau indexings.


The other speakers are the following:

Arvind Ayyer (CEA, Saclay) and Volker Strehl - (Universität Erlangen-Nürnberg)
Combinatorial properties of an asymmetric exclusion process

Matthieu Deneufchâtel  (LIPN, Université Paris 13)
Asymptotic of Seilberg-like integrals: the unitary case and the binomial transform

Thomas Feierl -(INRIA Paris-Rocquencourt)
Asymptotics for reflectable lattice walks in a Weylchamber of type B

Valentin Féray- (Université Bordeaux 1)
Asymptotic of characters of symmetric groups and limit shape of Young diagrams

Roberta Fulci - (Università di Bologna)
Models and refined models for involutory reflection groups and classical Weyl groups

Florent Hivert - (LITIS Université de Rouen)
The Sage-Combinat Project: Status and future

Masao Ishikawa - (Tottori University)
A partial proof of Okada's conjecture for double-tailed diamonds

Matthieu Josuat-Vergès  - (Université Paris XI)
Genocchi numbers and alternative tableaux

Jang Soo Kim - (University of Paris 7)
Some results on permutation tableaux

Ricardo Mamede - (Universidade de Coimbra)
On the full interval of linear expansion of a skew Schur function

Luca Moci - (Università di Roma 3)
Toric arrangements and Tutte polynomials

Philippe Nadeau - (University of Vienna)
Polynomials around the Razumov Stroganov conjecture

Anne  Schilling - (University of California at Davis) and Nicolas Thiery - (Université Paris Sud)
Sorting monoids on Coxeter groups

Christian Stump - (LaCIM, Université du Québec à Montréal)
A cyclic sieving phenomenon in Catalan combinatorics