The quasisymmetric flag variety: a toric complex on noncrossing partitions

2025/08/16 by Bergeron, Nantel, Gagnon, Lucas, Nadeau, Philippe +2 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.12171

Abstract

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 of noncrossing partitions, and whose cohomology ring is the ring of quasisymmetric coinvariants.

Citations

• Equivariant quasisymmetry and noncrossing partitions
• The geometry of quasisymmetric coinvariants
• The HHMP decomposition of the permutohedron and degenerations of torus orbits in flag varieties
• Forest polynomials and the class of the permutahedral variety
• The excedance quotient of the Bruhat order, Quasisymmetric Varieties and Temperley-Lieb algebras
• Remixed Eulerian numbers
• Torus orbit closures in the flag variety
• Polypositroids
• The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope
• Bruhat Interval Polytopes
• Computation of generalized equivariant cohomologies of Kac-Moody flag varieties
• Smoothness of Schubert varieties via patterns in root systems
• Lower bounds for Kazhdan-Lusztig polynomials from patterns
• Positivity in equivariant Schubert calculus

Cited by

• Richardson tableaux and Schubert positivity

Related

• Equivariant quasisymmetry and noncrossing partitions
• Spaces of quasi-maps into the flag varieties and their applications
• The geometry of quasisymmetric coinvariants
• On toric degenerations of flag varieties
• Quasi-flag manifolds and moment graphs