6 papers · 1 filter
Jack Content Operators and the Deformed Algebra
Jean-Yves Thibon
Frenkel and Wang obtained a representation of the Virasoro algebra by commuting Goulden's cut-and-join operator with the Heisenberg generators. A vertex-operator construction by La…
Shifted Macdonald Polynomials and the -Deformed Goulden--Jackson Product
Jean-Yves Thibon
In a preceding article, we introduced stable symmetric series encoding simultaneously the normalized conjugacy classes of all symmetric groups. The same rational series remain stab…
Stable Symmetric Series, Differential Operators, and Jack Deformations
Jean-Yves Thibon
We introduce stable symmetric series which encode normalized conjugacy classes and their multiplication operators simultaneously for all symmetric groups. This gives a direct route…
The noncommutative geode
Jean-Christophe Novelli, Jean-Yves Thibon
We investigate the geode and some of its generalizations from the point of view on noncommutative symmetric functions.
Noncommutative chromatic quasi-symmetric functions, Macdonald polynomials, and the Yang-Baxter equation
Jean-Christophe Novelli, Jean-Yves Thibon
As shown in our paper [JCTA 177 (2021), Paper No. 105305], the chromatic quasi-symmetric function of Shareshian-Wachs can be lifted to , the algebra of quasi-symmetric…
Acyclic orientations and Hessenberg varieties
Jean-Christophe Novelli, Jean-Yves Thibon
We exhibit a bijection between acyclic orientations of a Dyck graph and Tymoczko cells of a regular nilpotent Hessenberg variety. This implies the Shareshian-Wachs formula for the…