5 papers
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…
The asymptotic Plancherel formula and Lusztig's asymptotic algebra for
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 . To do so, we construct a balanced system of cell modules,…
Orientation of alcoves in affine Weyl groups
Nathan Chapelier-Laget
Let be an irreducible Weyl group and its affine Weyl group. In a previous work the author introduced an affine variety , called the Shi variety of $W_a…
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…
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…