6 papers
Formulas for Koornwinder polynomials
Laura Colmenarejo, Lucas Gagnon, Arun Ram
This paper provides formulas for Koornwinder polynomials in analogy with the creation formula, the alcove walk formula and the non-attacking fillings formula for the type Ma…
When are Hopf algebras determined by integer sequences?
Nicolas Andrews, Lucas Gagnon, Félix Gélinas +2
We study the category of graded Hopf algebras that are free noncommutative, cocommutative, graded and connected from the perspective of the sequences of dimensions of the graded pi…
The Quasisymmetric Grassmannian
Nantel Bergeron, Lucas Gagnon, Hunter Spink +1
We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of -planes in . Each irreducible component is a positroid…
The Coxeter Flag Variety
Nantel Bergeron, Lucas Gagnon, Hunter Spink +1
For a Coxeter element in a Weyl group , we define the -Coxeter flag variety as the union of left-translated Richardson varieties $w^{-1}…
The quasisymmetric flag variety: a toric complex on noncrossing partitions
Nantel Bergeron, Lucas Gagnon, Philippe Nadeau +2
We develop the geometric theory of equivariant quasisymmetry via a new ``quasisymmetric flag variety''. This is a toric complex in the flag variety whose fixed point set is the set…
Equivariant quasisymmetry and noncrossing partitions
Nantel Bergeron, Lucas Gagnon, Philippe Nadeau +2
We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of…